Edit Profile (opens in new tab) Waldschmidt, Michel Co-Author Distance Author ID: waldschmidt.michel Published as: Waldschmidt, Michel; Waldschmidt, M. Further Spellings: Вальдшмидт Мичел Homepage: https://webusers.imj-prg.fr/~michel.waldschmidt/index2.html External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr Videos: carmin.tv Member of Collective: Parent, D. P. Documents Indexed: 211 Publications since 1970, including 8 Books and 6 Additional arXiv Preprints 9 Contributions as Editor · 4 Further Contributions Reviewing Activity: 408 Reviews Biographic References: 2 Publications Co-Authors: 54 Co-Authors with 68 Joint Publications 1,820 Co-Co-Authors all top 5 Co-Authors 151 single-authored 12 Levesque, Claude 10 Mignotte, Maurice 8 Bertrand, Daniel 7 Roy, Damien 6 Philippon, Patrice 5 Fouvry, Etienne 3 Langevin, Michel 3 Laurent, Michel 3 Serre, Jean-Pierre 2 Balasubramanian, Ramachandran 2 Brownawell, W. Dale 2 Gramain, Francois 2 Kumar, K. Senthil 2 Luca, Florian 2 Luck, Jean-Marc 2 Moussa, Pierre 2 Murthy, M. Pavaman 2 Shorey, Tarlok Nath 2 Soundararajan, Kannan 2 Thangadurai, Ravindranathan 2 Vaidya, Prabhakar G. 2 van der Poorten, Alfred J. 2 Zhu, Yaochen 1 Agarwal, Ashok Kumar 1 Amoroso, Francesco Antonio 1 Banyaga, Augustin 1 Bardos, Claude Williams 1 Berndt, Bruce Carl 1 Brindza, Béla 1 Brown, Martin L. 1 Bugeaud, Yann 1 Bundschuh, Peter 1 Cartier, Pierre 1 Charpentier, Éric 1 Choudary, A. D. R. 1 Cijsouw, Pieter Leendert 1 David, Guy 1 Di Vizio, Lucia 1 Emsalem, Michel 1 Fontaine, Jean-Marc 1 Fresnel, Jean 1 Gangbo, Wilfrid 1 Girard, Jean-Yves 1 Godefroy, Gilles 1 Habsieger, Laurent 1 Hindry, Marc 1 Huttner, Marc 1 Itzykson, Claude 1 Jackson, Allyn 1 Jiménez-Urroz, Jorge 1 Jutila, Matti Ilmari 1 Kanemitsu, Shigeru 1 Karoubi, Max 1 Krattenthaler, Christian Friedrich 1 Loxton, John H. 1 Morain, François 1 Moreau, Jean-Charles 1 Mullen, Gary L. 1 Murty, Vijaya Kumar 1 Nesterenko, Yuriĭ Valentinovich 1 Neudauer, Nancy Ann 1 Nikol’skiĭ, Nikolaĭ Kapitonovich 1 Persson, Ulf A. 1 Pintér, Ákos 1 Ramachandra, Kanakanahalli 1 Raynaud, Michel 1 Rémond, Guy 1 Reyssat, Eric 1 Schlickewei, Hans Peter 1 Schmidt, Wolfgang M. 1 Shparlinski, Igor E. 1 Shubin, Carol Ann 1 Tenenbaum, Gérald 1 Thakur, Dinesh S. 1 Villani, Cédric all top 5 Serials 11 Acta Arithmetica 7 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 4 Hardy-Ramanujan Journal 3 Compositio Mathematica 3 Comptes Rendus Mathématiques de l’Académie des Sciences 3 The Ramanujan Journal 3 Lecture Notes in Mathematics 3 Mathematics Newsletter 2 Journal d’Analyse Mathématique 2 Bulletin de la Société Mathématique de France 2 Gazette des Mathématiciens 2 Journal of Number Theory 2 Mathematika 2 Publicationes Mathematicae Debrecen 2 L’Enseignement Mathématique. 2e Série 2 Journal of the Australian Mathematical Society. Series A 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 European Mathematical Society Newsletter 2 Astérisque 2 Moscow Journal of Combinatorics and Number Theory 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Bulletin of the Australian Mathematical Society 1 Rocky Mountain Journal of Mathematics 1 Acta Mathematica 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Annales des Sciences Mathématiques du Québec 1 Archiv der Mathematik 1 The Australian Mathematical Society Gazette 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 The Journal of the Indian Mathematical Society. New Series 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Annalen 1 The Mathematics Student 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 1 Bulletin of the Greek Mathematical Society 1 Southeast Asian Bulletin of Mathematics 1 Acta Mathematica Hungarica 1 Journal of the Ramanujan Mathematical Society 1 Science in China. Series A 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 Istanbul Üniversitesi Fen Fakültesi Matematik Dergisi 1 Fiziko-Matematichesko Spisanie 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Notices of the American Mathematical Society 1 Computational Complexity 1 Vietnam Journal of Mathematics 1 Annals of Mathematics. Second Series 1 La Gaceta de la Real Sociedad Matemática Española 1 Journal of the Australian Mathematical Society 1 Moscow Mathematical Journal 1 Doğa. Turkish Journal of Mathematics 1 Bulletin de la Société Mathématique de France. Supplément. Mémoires 1 Pure and Applied Mathematics Quarterly 1 The Journal of Prime Research in Mathematics 1 Aspects of Mathematics 1 Contemporary Mathematics 1 Grundlehren der Mathematischen Wissenschaften 1 IMSc Report 1 Progress in Mathematics 1 Springer Proceedings in Physics 1 SMF Journée Annuelle 1 Uniform Distribution Theory 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Afrika Matematika 1 Springer Proceedings in Mathematics & Statistics 1 Transactions of the American Mathematical Society. Series B 1 Journal of Ramanujan Society of Mathematics and Mathematical Sciences 1 Trends in Mathematics 1 Le Sel et le Fer all top 5 Fields 205 Number theory (11-XX) 41 Algebraic geometry (14-XX) 20 Functions of a complex variable (30-XX) 16 Several complex variables and analytic spaces (32-XX) 14 History and biography (01-XX) 12 Special functions (33-XX) 11 General and overarching topics; collections (00-XX) 6 Field theory and polynomials (12-XX) 4 Group theory and generalizations (20-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Combinatorics (05-XX) 3 Approximations and expansions (41-XX) 2 Associative rings and algebras (16-XX) 2 Convex and discrete geometry (52-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 145 Publications have been cited 999 times in 665 Documents Cited by ▼ Year ▼ Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables. Zbl 0944.11024 Waldschmidt, Michel 137 2000 Lectures on the Mordell-Weil theorem. Transl. and ed. by Martin Brown from notes by Michel Waldschmidt. Zbl 0676.14005 Serre, Jean-Pierre 102 1989 Nombres transcendants. Zbl 0302.10030 Waldschmidt, Michel 61 1974 Nombres transcendants et groupes algébriques. Complete par deux appendices de Daniel Bertrand et Jean-Pierre Serre. Zbl 0428.10017 Waldschmidt, Michel 47 1979 A lower bound for linear forms in logarithms. Zbl 0357.10017 Waldschmidt, Michel 44 1980 Multiple zeta values: an introduction. (Valeurs zêta multiples. Une introduction.) Zbl 0976.11037 Waldschmidt, Michel 38 2000 Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt. Zbl 0966.11032 36 2001 Transcendance et exponentielles en plusieurs variables. Zbl 0454.10020 Waldschmidt, Michel 30 1981 Propriétés arithmétiques de fonctions de plusieurs variables. II. Zbl 0363.32003 Waldschmidt, Michel 30 1977 Linear forms in two logarithms and Schneider’s method. Zbl 0349.10029 Mignotte, Maurice; Waldschmidt, Michel 25 1978 Linear forms in logarithms on commutative algebraic groups. (Formes linéaires de logarithmes sur les groupes algébriques commutatifs.) Zbl 0651.10023 Philippon, Patrice; Waldschmidt, Michel 21 1988 From number theory to physics. Lectures of a meeting on number theory and physics held at the Centre de Physique, Les Houches (France), March 7-16, 1989. Zbl 0784.00021 21 1992 Linear forms in two logarithms and Schneider’s method. III. Zbl 0702.11044 Mignotte, Maurice; Waldschmidt, Michel 17 1989 Multiple polylogarithms: an introduction. Zbl 1035.11033 Waldschmidt, M. 17 2002 Linear independence of logarithms of algebraic numbers (with an appendix by M. Laurent). Zbl 0809.11038 Waldschmidt, Michel 16 1992 Lower bounds for linear forms in logarithms of algebraic numbers. (Minorations de combinaisons linéaires de logarithmes de nombres algébriques.) Zbl 0774.11036 Waldschmidt, Michel 15 1993 Transcendence of periods: the state of the art. Zbl 1220.11090 Waldschmidt, Michel 15 2006 Lower bounds for linear forms in logarithms. Zbl 0659.10037 Philippon, P.; Waldschmidt, M. 14 1988 Solution du huitieme problème de Schneider. Zbl 0262.10021 Waldschmidt, Michel 13 1973 Transcendence measures for exponentials and logarithms. Zbl 0388.10022 Waldschmidt, Michel 13 1978 Polya’s theorem by Schneider’s method. Zbl 0381.10029 Waldschmidt, M. 12 1978 Algebraic values of analytic functions. Zbl 1062.11049 Waldschmidt, Michel 12 2003 On algebraic numbers of small height: Linear forms in one logarithm. Zbl 0801.11033 Mignotte, Maurice; Waldschmidt, Michel 11 1994 Recent advances in Diophantine approximation. Zbl 1271.11070 Waldschmidt, Michel 10 2012 On the transcendence methods of Gelfond and Schneider in several variables. Zbl 0659.10035 Waldschmidt, M. 10 1988 Open Diophantine problems. Zbl 1066.11030 Waldschmidt, Michel 10 2004 Linear forms and simultaneous approximations. Zbl 0345.10021 Cijsouw, Pieter L.; Waldschmidt, Michel 10 1977 Sous-groupes analytiques de groupes algébriques. Zbl 0579.14039 Waldschmidt, Michel 9 1983 Simultaneous approximation of numbers connected with the exponential function. Zbl 0388.10023 Waldschmidt, Michel 9 1978 Liouville numbers and Schanuel’s conjecture. Zbl 1294.11120 Kumar, K. Senthil; Thangadurai, R.; Waldschmidt, M. 9 2014 Simultaneous linear forms in logarithms on commutative algebraic groups. (Formes linéaires de logarithmes simultanées sur les groupes algébriques commutatifs.) Zbl 0681.10024 Philippon, P.; Waldschmidt, M. 8 1988 Nombres transcendants et groupes algébriques. (Transcendental numbers and algebraic groups). Complété par deux appendices de Daniel Bertrand et Jean-Pierre Serre. 2e éd. Zbl 0621.10022 Waldschmidt, Michel 8 1987 Diophantine approximation in commutative algebraic groups. I: An effective version of the algebraic subgroup. (Approximation diophantienne dans les groupes algébriques commutatifs. I: Une version effective du sous-groupe algébrique.) Zbl 0880.11054 Waldschmidt, Michel 8 1997 Simultaneous approximation and algebraic independence. Zbl 0916.11042 Roy, Damien; Waldschmidt, Michel 7 1997 Transcendence methods. Zbl 0432.10016 Waldschmidt, Michel 7 1979 Diophantine approximation and algebraic independence of logarithms. (Approximation diophantienne et indépendance algébrique de logarithmes.) Zbl 0895.11030 Roy, Damien; Waldschmidt, Michel 7 1997 Valeurs algébriques de fonctions analytiques. (Algebraic values of analytic functions). Zbl 0553.10026 Gramain, François; Mignotte, Maurice; Waldschmidt, Michel 7 1986 On the arithmetic nature of the values of modular functions. (Sur la nature arithmétique des valeurs de fonctions modulaires.) Zbl 0908.11029 Waldschmidt, Michel 6 1997 Linear forms in two logarithms and Schneider’s method. II. Zbl 0642.10034 Mignotte, Maurice; Waldschmidt, Michel 6 1989 Number theory and physics. Proceedings of the winter school, Les Houches, France, March 7–16, 1989. Zbl 0702.00008 6 1990 Groupes algébriques et grands degrés de transcendance. Appendice: Déformation d’un groupe algébrique par J. Fresnel. (Algebraic groups and large transcendence degrees). Zbl 0592.10028 Waldschmidt, Michel 6 1986 Algebraic independence of values of exponential functions. (Indépendance algébrique des valeurs de la fonction exponentielle.) Zbl 0224.10033 Waldschmidt, Michel 6 1971 On the representation of integers by cyclotomic forms with large degree. (Sur la représentation des entiers par les formes cyclotomiques de grand degré.) Zbl 1455.11066 Fouvry, Étienne; Waldschmidt, Michel 6 2020 On the maximal length of two sequences of consecutive integers with the same prime divisors. Zbl 0689.10049 Balasubramanian, R.; Shorey, T. N.; Waldschmidt, M. 5 1989 Formes linéaires de logarithmes elliptiques et mesures de transcendance. (Linear forms in elliptic logarithms and transcendence measures). Zbl 0692.10035 Philippon, Patrice; Waldschmidt, Michel 5 1989 Approximations diophantiennes et nombres transcendants. Colloque de Luminy, 1982. Zbl 0504.00005 5 1983 Quadratic relations between logarithms of algebraic numbers. Zbl 0860.11040 Roy, Damien; Waldschmidt, Michel 5 1995 Approximation des valeurs de fonctions transcendantes. Zbl 0305.10027 Mignotte, Maurice; Waldschmidt, Michel 5 1975 Elliptic functions and transcendence. Zbl 1210.11084 Waldschmidt, Michel 5 2008 Representation of integers by cyclotomic binary forms. Zbl 1417.11028 Fouvry, Étienne; Levesque, Claude; Waldschmidt, Michel 5 2018 Indépendance algébrique de nombres de Liouville. (Algebraic independence of Liouville numbers). Zbl 0729.11035 Waldschmidt, Michel 5 1990 Algebraic independence of transcendental numbers. Gel’fond’s method and its developments. Zbl 0556.10023 Waldschmidt, Michel 5 1984 Families of Thue-Mahler equations having only trivial solutions. (Familles d’équations de Thue-Mahler n’ayant que des solutions triviales.) Zbl 1304.11016 Levesque, Claude; Waldschmidt, Michel 4 2012 Half a century of transcendence. (Un demi-siècle de transcendance.) Zbl 0977.11030 Waldschmidt, Michel 4 2000 Sur certains characteres du groupe des classes d’ideles d’un corps du nombres. Zbl 0494.12007 Waldschmidt, Michel 4 1982 Propriétés arithmétiques des valeurs de fonctions méromorphes algébriquement indépendantes. (Arithmetic properties of the values of algebraically independent meromorphic functions.). Zbl 0227.10022 Waldschmidt, Michel 4 1973 Les travaux de G. V. Chudnovskiĭ sur les nombres transcendants. Zbl 0345.10020 Waldschmidt, Michel 4 1977 The algebraic independence of certain numbers to algebraic powers. Zbl 0357.10018 Brownawell, W. D.; Waldschmidt, M. 4 1977 Nombres transcendants et fonctions sigma de Weierstrass. Zbl 0402.10037 Waldschmidt, Michel 4 1979 Solution d’un problème de Schneider sur les nombres transcendants. Zbl 0206.05703 Waldschmidt, M. 4 1970 Diophantine approximation by conjugate algebraic integers. Zbl 1055.11043 Roy, Damien; Waldschmidt, Michel 4 2004 A family of Thue equations involving powers of units of the simplest cubic fields. Zbl 1395.11059 Levesque, Claude; Waldschmidt, Michel 4 2015 Dependence of logarithms of algebraic points. Zbl 0714.11043 Waldschmidt, M. 4 1990 Nouvelles méthodes pour minorer des combinaisons linéaires de logarithmes de nombres algébriques. (New methods for lower bounds of linear forms in logarithms of algebraic numbers). Zbl 0733.11020 Waldschmidt, Michel 4 1991 Matrices of finite abelian groups, finite Fourier transform and codes. Zbl 1331.20003 Kanemitsu, Shigeru; Waldschmidt, Michel 4 2013 Families of cubic Thue equations with effective bounds for the solutions. Zbl 1358.11050 Levesque, Claude; Waldschmidt, Michel 3 2013 Dependance de logarithmes dans les groupes algébriques. Zbl 0513.14028 Waldschmidt, M. 3 1983 Transcendental numbers and functions of several variables. Zbl 0791.11032 Waldschmidt, Michel 3 1993 Transcendence problems connected with Drinfeld modules. Zbl 0802.11023 Waldschmidt, M. 3 1990 Auxiliary functions and analytical functionals. I. (Fonctions auxiliaires et fonctionnelles analytiques. I.) Zbl 0742.11035 Waldschmidt, Michel 3 1991 Approximation simultanee de valeurs de la fonction exponentielle. Zbl 0345.10022 Mignotte, Maurice; Waldschmidt, Michel 3 1977 Variations on the six exponentials theorem. Zbl 1176.11033 Waldschmidt, Michel 3 2005 Density of rational points on an algebraic group. (Densité des points rationnels sur un groupe algébrique.) Zbl 0837.11040 Waldschmidt, Michel 3 1994 Lecture on the \(abc\) conjecture and some of its consequences. Zbl 1395.11056 Waldschmidt, Michel 3 2015 Hopf algebras and transcendental numbers. Zbl 1170.11315 Waldschmidt, Michel 3 2005 A lower bound for the p-adic rank of the units of an algebraic number field. Zbl 0541.12003 Waldschmidt, M. 3 1984 Density measure of rational points on Abelian varieties. Zbl 0931.11020 Waldschmidt, Michel 3 1999 Simultaneous Fermat-Pell-Mahler equations. (Équations de Fermat-Pell-Mahler simultanées.) Zbl 1249.11053 Bugeaud, Yann; Levesque, Claude; Waldschmidt, Michel 3 2011 Parametric geometry of numbers in function fields. Zbl 1428.11126 Roy, Damien; Waldschmidt, Michel 3 2017 On the \(p\)-adic closure of a subgroup of rational points on an abelian variety. Zbl 1291.11104 Waldschmidt, Michel 3 2011 Integer valued functions on products. Zbl 0885.11048 Waldschmidt, Michel 3 1997 Families of Thue equations associated with a rank 1 subgroup of totally real units of a number field. (Familles d’équations de Thue associées à un sous-groupe de rang 1 d’unités totalement réelles d’un corps de nombres.) Zbl 1394.11030 Levesque, Claude; Waldschmidt, Michel 3 2015 Further variations on the six exponentials theorem. Zbl 1116.11054 Waldschmidt, Michel 3 2005 Schanuel’s conjecture: algebraic independence of transcendental numbers. Zbl 1387.11057 Waldschmidt, Michel 3 2015 Solving effectively some families of Thue Diophantine equations. Zbl 1352.11035 Levesque, Claude; Waldschmidt, Michel 3 2013 Solving simultaneously Thue equations in the almost totally imaginary case. Zbl 1418.11053 Levesque, Claude; Waldschmidt, Michel 3 2016 Zeros of linear recurrence sequences. Zbl 0926.11019 Schlickewei, Hans Peter; Schmidt, Wolfgang M.; Waldschmidt, Michel 2 1999 Irrationality results for theta functions by Gel’fond-Schneider’s method. Zbl 0642.10035 Bundschuh, Peter; Waldschmidt, Michel 2 1989 A generalisation of a transcendence criterion of Gel’fond to several variables. (Une généralisation en plusieurs variables d’un critère de transcendance de Gel’fond.) Zbl 0531.10037 Waldschmidt, Michel; Zhu, Yaochen 2 1983 A lower bound for linear forms in the logarithms of algebraic numbers. Zbl 0623.10023 Loxton, J. H.; Mignotte, M.; van der Poorten, A. J.; Waldschmidt, M. 2 1987 On the algebraic subgroup theorem. (Autour du théorème du sous-groupe algébrique.) Zbl 0813.11041 Roy, Damien; Waldschmidt, Michel 2 1993 Auxiliary functions and analytical functionals. II. (Fonctions auxiliaires et fonctionnelles analytiques. II.) Zbl 0742.11036 Waldschmidt, Michel 2 1991 On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors. Zbl 0859.11012 Balasubramanian, R.; Langevin, M.; Shorey, T. N.; Waldschmidt, M. 2 1996 Extrapolation with interpolation determinants. Zbl 0938.11040 Waldschmidt, Michel 2 1998 Transcendence and algebraic independence of values of modular functions. (Transcendance et indépendance algébrique de valeurs de fonctions modulaires.) Zbl 0930.11055 Waldschmidt, Michel 2 1999 On the distribution of solutions of Thue’s equation. Zbl 0934.11014 Brindza, Béla; Pintér, Ákos; van der Poorten, Alfred J.; Waldschmidt, Michel 2 1999 Integer valued entire functions on Cartesian products. Zbl 0941.11028 Waldschmidt, Michel 2 1999 Algebraic independence of values of exponential and elliptic functions. Zbl 0616.10029 Waldschmidt, Michel 2 1986 Words and transcendence. Zbl 1195.11095 Waldschmidt, Michel 2 2009 Petits degrés de transcendance par la méthode de Schneider en une variable. (Small transcendence degrees obtained by Schneider’s method in one variable). Zbl 0571.10034 Waldschmidt, Michel 2 1985 Number of integers represented by families of binary forms. I. Zbl 1536.11071 Fouvry, Étienne; Waldschmidt, Michel 1 2023 The four exponentials problem and Schanuel’s conjecture. Zbl 1543.11060 Waldschmidt, Michel 1 2023 Lidstone interpolation. I: One variable. Zbl 1536.30059 Waldschmidt, Michel 1 2022 On entire functions of several variables with derivatives of even order taking integer values. Zbl 1492.32002 Waldschmidt, Michel 1 2021 On transcendental entire functions with infinitely many derivatives taking integer values at two points. Zbl 1488.30174 Waldschmidt, M. 1 2021 On the representation of integers by cyclotomic forms with large degree. (Sur la représentation des entiers par les formes cyclotomiques de grand degré.) Zbl 1455.11066 Fouvry, Étienne; Waldschmidt, Michel 6 2020 Thue Diophantine equations. Zbl 1456.11034 Waldschmidt, Michel 2 2020 Representation of integers by cyclotomic binary forms. Zbl 1417.11028 Fouvry, Étienne; Levesque, Claude; Waldschmidt, Michel 5 2018 Parametric geometry of numbers in function fields. Zbl 1428.11126 Roy, Damien; Waldschmidt, Michel 3 2017 Families of Thue equations associated with a rank one subgroup of the unit group of a number field. Zbl 1428.11060 Levesque, Claude; Waldschmidt, Michel 1 2017 Solving simultaneously Thue equations in the almost totally imaginary case. Zbl 1418.11053 Levesque, Claude; Waldschmidt, Michel 3 2016 A family of Thue equations involving powers of units of the simplest cubic fields. Zbl 1395.11059 Levesque, Claude; Waldschmidt, Michel 4 2015 Lecture on the \(abc\) conjecture and some of its consequences. Zbl 1395.11056 Waldschmidt, Michel 3 2015 Families of Thue equations associated with a rank 1 subgroup of totally real units of a number field. (Familles d’équations de Thue associées à un sous-groupe de rang 1 d’unités totalement réelles d’un corps de nombres.) Zbl 1394.11030 Levesque, Claude; Waldschmidt, Michel 3 2015 Schanuel’s conjecture: algebraic independence of transcendental numbers. Zbl 1387.11057 Waldschmidt, Michel 3 2015 Tell me about \(\ldots\) a period. (Raconte-moi \(\ldots\) une période.) Zbl 1358.11003 Waldschmidt, M. 2 2015 Liouville numbers, Liouville sets and Liouville fields. Zbl 1320.11065 Kumar, K. Senthil; Thangadurai, R.; Waldschmidt, M. 1 2015 Mathematics in the 21st century. Selected papers based on the presentations at the 6th world conference on 21st century mathematics, Lahore, Pakistan, March 6–9, 2013. Zbl 1304.00043 1 2015 Liouville numbers and Schanuel’s conjecture. Zbl 1294.11120 Kumar, K. Senthil; Thangadurai, R.; Waldschmidt, M. 9 2014 Matrices of finite abelian groups, finite Fourier transform and codes. Zbl 1331.20003 Kanemitsu, Shigeru; Waldschmidt, Michel 4 2013 Families of cubic Thue equations with effective bounds for the solutions. Zbl 1358.11050 Levesque, Claude; Waldschmidt, Michel 3 2013 Solving effectively some families of Thue Diophantine equations. Zbl 1352.11035 Levesque, Claude; Waldschmidt, Michel 3 2013 Recent advances in Diophantine approximation. Zbl 1271.11070 Waldschmidt, Michel 10 2012 Families of Thue-Mahler equations having only trivial solutions. (Familles d’équations de Thue-Mahler n’ayant que des solutions triviales.) Zbl 1304.11016 Levesque, Claude; Waldschmidt, Michel 4 2012 Approximation of an algebraic number by products of rational numbers and units. Zbl 1300.11026 Levesque, Claude; Waldschmidt, Michel 1 2012 Questions of transcendence: big conjectures, little progress. (Questions de transcendance: grandes conjectures, petits progrès.) Zbl 1362.11068 Waldschmidt, Michel 1 2012 Simultaneous Fermat-Pell-Mahler equations. (Équations de Fermat-Pell-Mahler simultanées.) Zbl 1249.11053 Bugeaud, Yann; Levesque, Claude; Waldschmidt, Michel 3 2011 On the \(p\)-adic closure of a subgroup of rational points on an abelian variety. Zbl 1291.11104 Waldschmidt, Michel 3 2011 Some remarks on Diophantine equations and Diophantine approximation. Zbl 1247.11041 Levesque, Claude; Waldschmidt, Michel 1 2011 Words and transcendence. Zbl 1195.11095 Waldschmidt, Michel 2 2009 Elliptic functions and transcendence. Zbl 1210.11084 Waldschmidt, Michel 5 2008 Transcendence of periods: the state of the art. Zbl 1220.11090 Waldschmidt, Michel 15 2006 Serge Lang’s contributions to the theory of transcendental numbers. (Les contributions de Serge Lang à la théorie des nombres transcendants.) Zbl 1164.01006 Waldschmidt, Michel 1 2006 Variations on the six exponentials theorem. Zbl 1176.11033 Waldschmidt, Michel 3 2005 Hopf algebras and transcendental numbers. Zbl 1170.11315 Waldschmidt, Michel 3 2005 Further variations on the six exponentials theorem. Zbl 1116.11054 Waldschmidt, Michel 3 2005 Open Diophantine problems. Zbl 1066.11030 Waldschmidt, Michel 10 2004 Diophantine approximation by conjugate algebraic integers. Zbl 1055.11043 Roy, Damien; Waldschmidt, Michel 4 2004 Algebraic values of analytic functions. Zbl 1062.11049 Waldschmidt, Michel 12 2003 Linear independence measures for logarithms of algebraic numbers. Zbl 1093.11054 Waldschmidt, Michel 1 2003 Multiple polylogarithms: an introduction. Zbl 1035.11033 Waldschmidt, M. 17 2002 Number theory and discrete mathematics. Proceedings of the international conference in honour of Srinivasa Ramanujan, Chandigarh, India, October 2–6, 2000. Zbl 0997.00018 1 2002 Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt. Zbl 0966.11032 36 2001 Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables. Zbl 0944.11024 Waldschmidt, Michel 137 2000 Multiple zeta values: an introduction. (Valeurs zêta multiples. Une introduction.) Zbl 0976.11037 Waldschmidt, Michel 38 2000 Half a century of transcendence. (Un demi-siècle de transcendance.) Zbl 0977.11030 Waldschmidt, Michel 4 2000 On a problem of Mahler concerning the approximation of exponentials and logarithms. Zbl 1002.11061 Waldschmidt, Michel 1 2000 Algebraic independence of transcendental numbers: a survey. Zbl 1072.11510 Waldschmidt, Michel 1 2000 Density measure of rational points on Abelian varieties. Zbl 0931.11020 Waldschmidt, Michel 3 1999 Zeros of linear recurrence sequences. Zbl 0926.11019 Schlickewei, Hans Peter; Schmidt, Wolfgang M.; Waldschmidt, Michel 2 1999 Transcendence and algebraic independence of values of modular functions. (Transcendance et indépendance algébrique de valeurs de fonctions modulaires.) Zbl 0930.11055 Waldschmidt, Michel 2 1999 On the distribution of solutions of Thue’s equation. Zbl 0934.11014 Brindza, Béla; Pintér, Ákos; van der Poorten, Alfred J.; Waldschmidt, Michel 2 1999 Integer valued entire functions on Cartesian products. Zbl 0941.11028 Waldschmidt, Michel 2 1999 From simultaneous approximations to algebraic independence. Zbl 0930.11056 Waldschmidt, Michel 1 1999 Extrapolation with interpolation determinants. Zbl 0938.11040 Waldschmidt, Michel 2 1998 Diophantine approximation in commutative algebraic groups. I: An effective version of the algebraic subgroup. (Approximation diophantienne dans les groupes algébriques commutatifs. I: Une version effective du sous-groupe algébrique.) Zbl 0880.11054 Waldschmidt, Michel 8 1997 Simultaneous approximation and algebraic independence. Zbl 0916.11042 Roy, Damien; Waldschmidt, Michel 7 1997 Diophantine approximation and algebraic independence of logarithms. (Approximation diophantienne et indépendance algébrique de logarithmes.) Zbl 0895.11030 Roy, Damien; Waldschmidt, Michel 7 1997 On the arithmetic nature of the values of modular functions. (Sur la nature arithmétique des valeurs de fonctions modulaires.) Zbl 0908.11029 Waldschmidt, Michel 6 1997 Integer valued functions on products. Zbl 0885.11048 Waldschmidt, Michel 3 1997 On the maximal length of two sequences of integers in arithmetic progressions with the same prime divisors. Zbl 0859.11012 Balasubramanian, R.; Langevin, M.; Shorey, T. N.; Waldschmidt, M. 2 1996 Dependence of logarithms on commutative algebraic groups. Zbl 0883.11036 Waldschmidt, Michel 1 1996 Quadratic relations between logarithms of algebraic numbers. Zbl 0860.11040 Roy, Damien; Waldschmidt, Michel 5 1995 Density of rational points on an algebraic group. Errata. (Densité des points rationnels sur un groupe algébrique (errata).) Zbl 0853.11057 Waldschmidt, Michel 1 1995 On algebraic numbers of small height: Linear forms in one logarithm. Zbl 0801.11033 Mignotte, Maurice; Waldschmidt, Michel 11 1994 Density of rational points on an algebraic group. (Densité des points rationnels sur un groupe algébrique.) Zbl 0837.11040 Waldschmidt, Michel 3 1994 Lower bounds for linear forms in logarithms of algebraic numbers. (Minorations de combinaisons linéaires de logarithmes de nombres algébriques.) Zbl 0774.11036 Waldschmidt, Michel 15 1993 Transcendental numbers and functions of several variables. Zbl 0791.11032 Waldschmidt, Michel 3 1993 On the algebraic subgroup theorem. (Autour du théorème du sous-groupe algébrique.) Zbl 0813.11041 Roy, Damien; Waldschmidt, Michel 2 1993 From number theory to physics. Lectures of a meeting on number theory and physics held at the Centre de Physique, Les Houches (France), March 7-16, 1989. Zbl 0784.00021 21 1992 Linear independence of logarithms of algebraic numbers (with an appendix by M. Laurent). Zbl 0809.11038 Waldschmidt, Michel 16 1992 Constructions de fonctions auxiliaires. (Constructions of auxiliary functions). Zbl 0770.11038 Waldschmidt, Michel 1 1992 Nouvelles méthodes pour minorer des combinaisons linéaires de logarithmes de nombres algébriques. (New methods for lower bounds of linear forms in logarithms of algebraic numbers). Zbl 0733.11020 Waldschmidt, Michel 4 1991 Auxiliary functions and analytical functionals. I. (Fonctions auxiliaires et fonctionnelles analytiques. I.) Zbl 0742.11035 Waldschmidt, Michel 3 1991 Auxiliary functions and analytical functionals. II. (Fonctions auxiliaires et fonctionnelles analytiques. II.) Zbl 0742.11036 Waldschmidt, Michel 2 1991 Number theory and physics. Proceedings of the winter school, Les Houches, France, March 7–16, 1989. Zbl 0702.00008 6 1990 Indépendance algébrique de nombres de Liouville. (Algebraic independence of Liouville numbers). Zbl 0729.11035 Waldschmidt, Michel 5 1990 Dependence of logarithms of algebraic points. Zbl 0714.11043 Waldschmidt, M. 4 1990 Transcendence problems connected with Drinfeld modules. Zbl 0802.11023 Waldschmidt, M. 3 1990 Cinquante ans de polynômes. Fifty years of polynomials. Proceedings of a conference held in honour of Alain Durand at the Institut Henri Poincaré, Paris, France, May 26-27, 1988. Zbl 0683.00011 1 1990 Algebraic independence of certain numbers related to Liouville numbers. Zbl 0697.10029 Waldschmidt, Michel; Zhu, Yaochen 1 1990 Sur l’équation de Pillai et la différence entre deux produits de puissances de nombres entiers. (On the Pillai equation and the difference between two products of powers of integers). Zbl 0733.11021 Waldschmidt, Michel 1 1990 Lectures on the Mordell-Weil theorem. Transl. and ed. by Martin Brown from notes by Michel Waldschmidt. Zbl 0676.14005 Serre, Jean-Pierre 102 1989 Linear forms in two logarithms and Schneider’s method. III. Zbl 0702.11044 Mignotte, Maurice; Waldschmidt, Michel 17 1989 Linear forms in two logarithms and Schneider’s method. II. Zbl 0642.10034 Mignotte, Maurice; Waldschmidt, Michel 6 1989 On the maximal length of two sequences of consecutive integers with the same prime divisors. Zbl 0689.10049 Balasubramanian, R.; Shorey, T. N.; Waldschmidt, M. 5 1989 Formes linéaires de logarithmes elliptiques et mesures de transcendance. (Linear forms in elliptic logarithms and transcendence measures). Zbl 0692.10035 Philippon, Patrice; Waldschmidt, Michel 5 1989 Irrationality results for theta functions by Gel’fond-Schneider’s method. Zbl 0642.10035 Bundschuh, Peter; Waldschmidt, Michel 2 1989 Linear forms in logarithms on commutative algebraic groups. (Formes linéaires de logarithmes sur les groupes algébriques commutatifs.) Zbl 0651.10023 Philippon, Patrice; Waldschmidt, Michel 21 1988 Lower bounds for linear forms in logarithms. Zbl 0659.10037 Philippon, P.; Waldschmidt, M. 14 1988 On the transcendence methods of Gelfond and Schneider in several variables. Zbl 0659.10035 Waldschmidt, M. 10 1988 Simultaneous linear forms in logarithms on commutative algebraic groups. (Formes linéaires de logarithmes simultanées sur les groupes algébriques commutatifs.) Zbl 0681.10024 Philippon, P.; Waldschmidt, M. 8 1988 Sur les méthodes de Schneider, Gel’fond et Baker. (On the methods of Schneider, Gel’fond and Baker). Zbl 0714.11042 Waldschmidt, Michel 1 1988 Some transcendental aspects of Ramanujan’s work. Zbl 0696.10029 Waldschmidt, Michel 1 1988 Nombres transcendants et groupes algébriques. (Transcendental numbers and algebraic groups). Complété par deux appendices de Daniel Bertrand et Jean-Pierre Serre. 2e éd. Zbl 0621.10022 Waldschmidt, Michel 8 1987 A lower bound for linear forms in the logarithms of algebraic numbers. Zbl 0623.10023 Loxton, J. H.; Mignotte, M.; van der Poorten, A. J.; Waldschmidt, M. 2 1987 Valeurs algébriques de fonctions analytiques. (Algebraic values of analytic functions). Zbl 0553.10026 Gramain, François; Mignotte, Maurice; Waldschmidt, Michel 7 1986 Groupes algébriques et grands degrés de transcendance. Appendice: Déformation d’un groupe algébrique par J. Fresnel. (Algebraic groups and large transcendence degrees). Zbl 0592.10028 Waldschmidt, Michel 6 1986 Algebraic independence of values of exponential and elliptic functions. Zbl 0616.10029 Waldschmidt, Michel 2 1986 Petits degrés de transcendance par la méthode de Schneider en une variable. (Small transcendence degrees obtained by Schneider’s method in one variable). Zbl 0571.10034 Waldschmidt, Michel 2 1985 ...and 45 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 674 Authors 39 Waldschmidt, Michel 20 Bugeaud, Yann 19 Dubickas, Artūras 16 Roy, Damien 15 Marques, Diego 11 Masser, David William 10 Mignotte, Maurice 10 Philippon, Patrice 8 Adamczewski, Boris 8 Laurent, Michel 8 Sha, Min 7 Ably, Mohammed 7 Diaz, Guy 7 Fischler, Stéphane 7 Harbourne, Brian 7 Hirata-Kohno, Noriko 7 Le, Maohua 7 Luca, Florian 7 Pethő, Attila 6 Rivoal, Tanguy 6 Tubbs, Robert 5 Amoroso, Francesco Antonio 5 Chalebgwa, Taboka Prince 5 Corvaja, Pietro 5 David, Sinnou 5 Escassut, Alain 5 Gaudron, Éric 5 Gramain, Francois 5 Moreira, Carlos Gustavo Tamm de Araujo 5 Murty, Maruti Ram 5 Rayaguru, Sai Gopal 5 Stewart, Cameron L. 5 Tzanakis, Nikos 5 Yu, Kunrui 5 Zannier, Umberto M. 4 Berenstein, Carlos Alberto 4 Bertrand, Daniel 4 Bradley, David M. 4 Bruinier, Jan Hendrik 4 Chirskiĭ, Vladimir Grigor’evich 4 de Weger, Benjamin M. M. 4 Gun, Sanoli 4 Levesque, Claude 4 Manchon, Dominique 4 Nakamaye, Michael 4 Pila, Jonathan 4 Schleischitz, Johannes 4 Seceleanu, Alexandra 4 Shorey, Tarlok Nath 4 Szemberg, Tomasz 4 Wüstholz, Gisbert 4 Zhu, Yaochen 4 Ziegler, Volker 3 Balakrishnan, Jennifer S. 3 Bosser, Vincent 3 Bouillot, Olivier 3 Brownawell, W. Dale 3 Caveny, Deanna M. 3 Cooper, Susan Marie 3 D’Hoker, Eric 3 Dumnicki, Marcin 3 Ebrahimi-Fard, Kurusch 3 Fouvry, Etienne 3 Glass, Andrew M. W. 3 Gómez, Carlos Alexis 3 Guardo, Elena 3 Habegger, Philipp 3 Koiran, Pascal 3 Kumar, K. Senthil 3 Lara Rodríguez, José Alejandro 3 Malara, Grzegorz 3 Mosunov, Anton S. 3 Panda, Gopal Krishna 3 Pellarin, Federico 3 Poels, Anthony 3 Ramirez, Josimar 3 Rath, Purusottam 3 Reyssat, Eric 3 Shmelev, Andrey A. 3 Simsek, Yilmaz 3 Smyth, Christopher J. 3 Szpond, Justyna 3 Tutaj-Gasińska, Halszka 3 Unterberger, Jérémie M. 3 Yger, Alain 3 Yu, Jing 2 Amou, Masaaki 2 Balasubramanian, Ramachandran 2 Barbagallo, María Laura 2 Bell, Jason P. 2 Berger, Arno 2 Bertolin, Cristiana 2 Bézivin, Jean-Paul 2 Bijlsma, Alex 2 Bilu, Yuri F. 2 Bisui, Sankhaneel 2 Bocci, Cristiano 2 Bowman, Douglas C. 2 Bravo, Jhon Jairo 2 Brown, Francis C. S. ...and 574 more Authors all top 5 Cited in 175 Serials 74 Journal of Number Theory 27 Journal de Théorie des Nombres de Bordeaux 21 Compositio Mathematica 18 Annales de l’Institut Fourier 15 Proceedings of the American Mathematical Society 14 Bulletin de la Société Mathématique de France 14 Monatshefte für Mathematik 12 Bulletin of the Australian Mathematical Society 12 Mathematical Notes 12 Inventiones Mathematicae 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 International Journal of Number Theory 11 Advances in Mathematics 10 Indagationes Mathematicae. New Series 10 The Ramanujan Journal 9 Mathematics of Computation 9 Acta Arithmetica 9 Journal of Pure and Applied Algebra 9 Mathematische Annalen 8 Transactions of the American Mathematical Society 8 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 8 Acta Mathematica Hungarica 7 Duke Mathematical Journal 7 Journal of Algebra 6 Archiv der Mathematik 6 Mathematika 6 Proceedings of the Japan Academy. Series A 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Rocky Mountain Journal of Mathematics 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Acta Mathematica 5 Manuscripta Mathematica 5 Results in Mathematics 5 Journal of Symbolic Computation 5 Journal of High Energy Physics 5 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 4 Communications in Mathematical Physics 4 Israel Journal of Mathematics 4 Journal d’Analyse Mathématique 4 Journal für die Reine und Angewandte Mathematik 4 Bulletin of the American Mathematical Society. New Series 4 Journal of the European Mathematical Society (JEMS) 4 Integers 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Mathematische Zeitschrift 3 Rendiconti del Seminario Matematico della Università di Padova 3 Journal of the Ramanujan Mathematical Society 3 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 3 Linear Algebra and its Applications 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Acta Mathematica Sinica. New Series 3 Journal of Mathematical Sciences (New York) 3 Boletín de la Sociedad Matemática Mexicana. Third Series 3 Documenta Mathematica 3 Annals of Mathematics. Second Series 3 Journal of the Australian Mathematical Society 3 European Journal of Mathematics 3 Research in Number Theory 2 Communications in Algebra 2 Computer Physics Communications 2 Lithuanian Mathematical Journal 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Nuclear Physics. B 2 Chaos, Solitons and Fractals 2 The Mathematical Intelligencer 2 Applied Mathematics and Computation 2 Canadian Mathematical Bulletin 2 Journal of Functional Analysis 2 Journal of Soviet Mathematics 2 Memoirs of the American Mathematical Society 2 Nagoya Mathematical Journal 2 Proceedings of the London Mathematical Society. Third Series 2 Theoretical Computer Science 2 Physica D 2 Revista Matemática Iberoamericana 2 L’Enseignement Mathématique. 2e Série 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 Applicable Algebra in Engineering, Communication and Computing 2 Experimental Mathematics 2 Journal of Algebraic Combinatorics 2 Annales Mathématiques Blaise Pascal 2 Bulletin des Sciences Mathématiques 2 Doklady Mathematics 2 Chebyshevskiĭ Sbornik 2 Logical Methods in Computer Science 2 Communications in Mathematics 2 Moscow Journal of Combinatorics and Number Theory 2 Research in the Mathematical Sciences 2 Transactions of the American Mathematical Society. Series B 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Periodica Mathematica Hungarica 1 Physica A 1 Physics Letters. A 1 Journal of Geometry and Physics 1 Acta Mathematica Vietnamica ...and 75 more Serials all top 5 Cited in 52 Fields 539 Number theory (11-XX) 109 Algebraic geometry (14-XX) 53 Functions of a complex variable (30-XX) 35 Special functions (33-XX) 33 Commutative algebra (13-XX) 27 Dynamical systems and ergodic theory (37-XX) 25 Computer science (68-XX) 23 Several complex variables and analytic spaces (32-XX) 19 Combinatorics (05-XX) 19 Quantum theory (81-XX) 18 Field theory and polynomials (12-XX) 9 Mathematical logic and foundations (03-XX) 9 Group theory and generalizations (20-XX) 9 Approximations and expansions (41-XX) 9 Probability theory and stochastic processes (60-XX) 8 History and biography (01-XX) 8 Ordinary differential equations (34-XX) 8 Manifolds and cell complexes (57-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Associative rings and algebras (16-XX) 7 Measure and integration (28-XX) 7 Difference and functional equations (39-XX) 7 Convex and discrete geometry (52-XX) 6 Topological groups, Lie groups (22-XX) 6 Numerical analysis (65-XX) 5 Nonassociative rings and algebras (17-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Differential geometry (53-XX) 4 Real functions (26-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Statistics (62-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 3 Geometry (51-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Partial differential equations (35-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 2 General topology (54-XX) 2 Relativity and gravitational theory (83-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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