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 Member of Collective: Parent, D. P. Documents Indexed: 212 Publications since 1970, including 7 Books and 9 Additional arXiv Preprints 9 Contributions as Editor · 4 Further Contributions Reviewing Activity: 401 Reviews Biographic References: 2 Publications Co-Authors: 54 Co-Authors with 68 Joint Publications 1,806 Co-Co-Authors all top 5 Co-Authors 152 single-authored 13 Levesque, Claude 10 Mignotte, Maurice 8 Bertrand, Daniel 7 Roy, Damien 6 Philippon, Patrice 5 Fouvry, Etienne 3 Langevin, Michel 3 Serre, Jean-Pierre 2 Balasubramanian, Ramachandran 2 Brownawell, W. Dale 2 Gramain, Francois 2 Kumar, K. Senthil 2 Laurent, Michel 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 10 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 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 206 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) 4 Approximations and expansions (41-XX) 3 Combinatorics (05-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 141 Publications have been cited 893 times in 587 Documents Cited by ▼ Year ▼ Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables. Zbl 0944.11024 Waldschmidt, Michel 104 2000 Lectures on the Mordell-Weil theorem. Transl. and ed. by Martin Brown from notes by Michel Waldschmidt. Zbl 0676.14005 Serre, Jean-Pierre 65 1989 Nombres transcendants. Zbl 0302.10030 Waldschmidt, Michel 58 1974 A lower bound for linear forms in logarithms. Zbl 0357.10017 Waldschmidt, Michel 42 1980 Nombres transcendants et groupes algébriques. Complete par deux appendices de Daniel Bertrand et Jean-Pierre Serre. Zbl 0428.10017 Waldschmidt, Michel 39 1979 Multiple zeta values: an introduction. (Valeurs zêta multiples. Une introduction.) Zbl 0976.11037 Waldschmidt, Michel 37 2000 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 24 1977 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 23 2001 Linear forms in two logarithms and Schneider’s method. Zbl 0349.10029 Mignotte, Maurice; Waldschmidt, Michel 22 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 Linear forms in two logarithms and Schneider’s method. III. Zbl 0702.11044 Mignotte, Maurice; Waldschmidt, Michel 17 1989 Linear independence of logarithms of algebraic numbers (with an appendix by M. Laurent). Zbl 0809.11038 Waldschmidt, Michel 15 1992 Multiple polylogarithms: an introduction. Zbl 1035.11033 Waldschmidt, M. 15 2002 Lower bounds for linear forms in logarithms. Zbl 0659.10037 Philippon, P.; Waldschmidt, M. 14 1988 Lower bounds for linear forms in logarithms of algebraic numbers. (Minorations de combinaisons linéaires de logarithmes de nombres algébriques.) Zbl 0774.11036 Waldschmidt, Michel 14 1993 Solution du huitieme problème de Schneider. Zbl 0262.10021 Waldschmidt, Michel 13 1973 Transcendence of periods: the state of the art. Zbl 1220.11090 Waldschmidt, Michel 13 2006 Transcendence measures for exponentials and logarithms. Zbl 0388.10022 Waldschmidt, Michel 13 1978 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 13 1992 Polya’s theorem by Schneider’s method. Zbl 0381.10029 Waldschmidt, M. 12 1978 Algebraic values of analytic functions. Zbl 1062.11049 Waldschmidt, Michel 11 2003 On algebraic numbers of small height: Linear forms in one logarithm. Zbl 0801.11033 Mignotte, Maurice; Waldschmidt, Michel 11 1994 Linear forms and simultaneous approximations. Zbl 0345.10021 Cijsouw, Pieter L.; Waldschmidt, Michel 10 1977 Open Diophantine problems. Zbl 1066.11030 Waldschmidt, Michel 10 2004 Recent advances in Diophantine approximation. Zbl 1271.11070 Waldschmidt, Michel 9 2012 Sous-groupes analytiques de groupes algébriques. Zbl 0579.14039 Waldschmidt, Michel 9 1983 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 Liouville numbers and Schanuel’s conjecture. Zbl 1294.11120 Kumar, K. Senthil; Thangadurai, R.; Waldschmidt, M. 8 2014 Valeurs algébriques de fonctions analytiques. (Algebraic values of analytic functions). Zbl 0553.10026 Gramain, François; Mignotte, Maurice; Waldschmidt, Michel 7 1986 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 Simultaneous approximation of numbers connected with the exponential function. Zbl 0388.10023 Waldschmidt, Michel 7 1978 Linear forms in two logarithms and Schneider’s method. II. Zbl 0642.10034 Mignotte, Maurice; Waldschmidt, Michel 6 1989 On the transcendence methods of Gelfond and Schneider in several variables. Zbl 0659.10035 Waldschmidt, M. 6 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. 6 1988 Algebraic independence of values of exponential functions. (Indépendance algébrique des valeurs de la fonction exponentielle.) Zbl 0224.10033 Waldschmidt, Michel 6 1971 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 transcendental numbers. Gel’fond’s method and its developments. Zbl 0556.10023 Waldschmidt, Michel 5 1984 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 On the arithmetic nature of the values of modular functions. (Sur la nature arithmétique des valeurs de fonctions modulaires.) Zbl 0908.11029 Waldschmidt, Michel 5 1997 Elliptic functions and transcendence. Zbl 1210.11084 Waldschmidt, Michel 5 2008 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 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 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 5 1987 Transcendence methods. Zbl 0432.10016 Waldschmidt, Michel 5 1979 Approximations diophantiennes et nombres transcendants. Colloque de Luminy, 1982. Zbl 0504.00005 4 1983 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 Solution d’un problème de Schneider sur les nombres transcendants. Zbl 0206.05703 Waldschmidt, M. 4 1970 Half a century of transcendence. (Un demi-siècle de transcendance.) Zbl 0977.11030 Waldschmidt, Michel 4 2000 Les travaux de G. V. Chudnovskiĭ sur les nombres transcendants. Zbl 0345.10020 Waldschmidt, Michel 4 1977 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 The algebraic independence of certain numbers to algebraic powers. Zbl 0357.10018 Brownawell, W. D.; Waldschmidt, M. 4 1977 Diophantine approximation by conjugate algebraic integers. Zbl 1055.11043 Roy, Damien; Waldschmidt, Michel 4 2004 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 Number theory and physics. Proceedings of the winter school, Les Houches, France, March 7–16, 1989. Zbl 0702.00008 4 1990 A family of Thue equations involving powers of units of the simplest cubic fields. Zbl 1395.11059 Levesque, Claude; Waldschmidt, Michel 4 2015 On the representation of integers by cyclotomic forms with large degree. Zbl 1455.11066 Fouvry, Étienne; Waldschmidt, Michel 4 2020 Representation of integers by cyclotomic binary forms. Zbl 1417.11028 Fouvry, Étienne; Levesque, Claude; Waldschmidt, Michel 4 2018 Matrices of finite abelian groups, finite Fourier transform and codes. Zbl 1331.20003 Kanemitsu, Shigeru; Waldschmidt, Michel 4 2013 Sur certains characteres du groupe des classes d’ideles d’un corps du nombres. Zbl 0494.12007 Waldschmidt, Michel 3 1982 Dependance de logarithmes dans les groupes algébriques. Zbl 0513.14028 Waldschmidt, M. 3 1983 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 Density of rational points on an algebraic group. (Densité des points rationnels sur un groupe algébrique.) Zbl 0837.11040 Waldschmidt, Michel 3 1994 Approximation simultanee de valeurs de la fonction exponentielle. Zbl 0345.10022 Mignotte, Maurice; Waldschmidt, Michel 3 1977 Hopf algebras and transcendental numbers. Zbl 1170.11315 Waldschmidt, Michel 3 2005 Variations on the six exponentials theorem. Zbl 1176.11033 Waldschmidt, Michel 3 2005 Further variations on the six exponentials theorem. Zbl 1116.11054 Waldschmidt, Michel 3 2005 Dependence of logarithms of algebraic points. Zbl 0714.11043 Waldschmidt, M. 3 1990 Indépendance algébrique de nombres de Liouville. (Algebraic independence of Liouville numbers). Zbl 0729.11035 Waldschmidt, Michel 3 1990 Auxiliary functions and analytical functionals. I. (Fonctions auxiliaires et fonctionnelles analytiques. I.) Zbl 0742.11035 Waldschmidt, Michel 3 1991 Integer valued functions on products. Zbl 0885.11048 Waldschmidt, Michel 3 1997 Nombres transcendants et fonctions sigma de Weierstrass. Zbl 0402.10037 Waldschmidt, Michel 3 1979 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 Simultaneous Fermat-Pell-Mahler equations. (Équations de Fermat-Pell-Mahler simultanées.) Zbl 1249.11053 Bugeaud, Yann; Levesque, Claude; Waldschmidt, Michel 3 2011 Solving effectively some families of Thue Diophantine equations. Zbl 1352.11035 Levesque, Claude; Waldschmidt, Michel 3 2013 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 On the \(p\)-adic closure of a subgroup of rational points on an abelian variety. Zbl 1291.11104 Waldschmidt, Michel 3 2011 Families of cubic Thue equations with effective bounds for the solutions. Zbl 1358.11050 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 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 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 Parametric geometry of numbers in function fields. Zbl 1428.11126 Roy, Damien; Waldschmidt, Michel 2 2017 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 Extrapolation with interpolation determinants. Zbl 0938.11040 Waldschmidt, Michel 2 1998 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 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 Algebraic independence of values of exponential and elliptic functions. Zbl 0616.10029 Waldschmidt, Michel 2 1986 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 Auxiliary functions and analytical functionals. II. (Fonctions auxiliaires et fonctionnelles analytiques. II.) Zbl 0742.11036 Waldschmidt, Michel 2 1991 On the algebraic subgroup theorem. (Autour du théorème du sous-groupe algébrique.) Zbl 0813.11041 Roy, Damien; Waldschmidt, Michel 2 1993 Schanuel’s conjecture: algebraic independence of transcendental numbers. Zbl 1387.11057 Waldschmidt, Michel 2 2015 The four exponentials problem and Schanuel’s conjecture. Zbl 07773782 Waldschmidt, Michel 1 2023 On transcendental entire functions with infinitely many derivatives taking integer values at two points. Zbl 1488.30174 Waldschmidt, M. 1 2021 On entire functions of several variables with derivatives of even order taking integer values. Zbl 1492.32002 Waldschmidt, Michel 1 2021 On the representation of integers by cyclotomic forms with large degree. Zbl 1455.11066 Fouvry, Étienne; Waldschmidt, Michel 4 2020 Thue Diophantine equations. Zbl 1456.11034 Waldschmidt, Michel 1 2020 Representation of integers by cyclotomic binary forms. Zbl 1417.11028 Fouvry, Étienne; Levesque, Claude; Waldschmidt, Michel 4 2018 Parametric geometry of numbers in function fields. Zbl 1428.11126 Roy, Damien; Waldschmidt, Michel 2 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 2 2015 Tell me about \(\ldots\) a period. (Raconte-moi \(\ldots\) une période.) Zbl 1358.11003 Waldschmidt, M. 1 2015 Liouville numbers, Liouville sets and Liouville fields. Zbl 1320.11065 Kumar, K. Senthil; Thangadurai, R.; Waldschmidt, M. 1 2015 Liouville numbers and Schanuel’s conjecture. Zbl 1294.11120 Kumar, K. Senthil; Thangadurai, R.; Waldschmidt, M. 8 2014 Matrices of finite abelian groups, finite Fourier transform and codes. Zbl 1331.20003 Kanemitsu, Shigeru; Waldschmidt, Michel 4 2013 Solving effectively some families of Thue Diophantine equations. Zbl 1352.11035 Levesque, Claude; Waldschmidt, Michel 3 2013 Families of cubic Thue equations with effective bounds for the solutions. Zbl 1358.11050 Levesque, Claude; Waldschmidt, Michel 3 2013 Recent advances in Diophantine approximation. Zbl 1271.11070 Waldschmidt, Michel 9 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 Questions of transcendence: big conjectures, little progress. (Questions de transcendance: grandes conjectures, petits progrès.) Zbl 1362.11068 Waldschmidt, Michel 1 2012 Approximation of an algebraic number by products of rational numbers and units. Zbl 1300.11026 Levesque, Claude; 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 13 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 Hopf algebras and transcendental numbers. Zbl 1170.11315 Waldschmidt, Michel 3 2005 Variations on the six exponentials theorem. Zbl 1176.11033 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 11 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. 15 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 23 2001 Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables. Zbl 0944.11024 Waldschmidt, Michel 104 2000 Multiple zeta values: an introduction. (Valeurs zêta multiples. Une introduction.) Zbl 0976.11037 Waldschmidt, Michel 37 2000 Half a century of transcendence. (Un demi-siècle de transcendance.) Zbl 0977.11030 Waldschmidt, Michel 4 2000 Algebraic independence of transcendental numbers: a survey. Zbl 1072.11510 Waldschmidt, Michel 1 2000 On a problem of Mahler concerning the approximation of exponentials and logarithms. Zbl 1002.11061 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 5 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 14 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 Linear independence of logarithms of algebraic numbers (with an appendix by M. Laurent). Zbl 0809.11038 Waldschmidt, Michel 15 1992 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 13 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 4 1990 Dependence of logarithms of algebraic points. Zbl 0714.11043 Waldschmidt, M. 3 1990 Indépendance algébrique de nombres de Liouville. (Algebraic independence of Liouville numbers). Zbl 0729.11035 Waldschmidt, Michel 3 1990 Transcendence problems connected with Drinfeld modules. Zbl 0802.11023 Waldschmidt, M. 3 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 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 Lectures on the Mordell-Weil theorem. Transl. and ed. by Martin Brown from notes by Michel Waldschmidt. Zbl 0676.14005 Serre, Jean-Pierre 65 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. 6 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. 6 1988 Some transcendental aspects of Ramanujan’s work. Zbl 0696.10029 Waldschmidt, Michel 1 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 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 5 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 Algebraic independence of transcendental numbers. Gel’fond’s method and its developments. Zbl 0556.10023 Waldschmidt, Michel 5 1984 A lower bound for the p-adic rank of the units of an algebraic number field. Zbl 0541.12003 Waldschmidt, M. 3 1984 Les nombres transcendants. Zbl 0548.10021 Bertrand, D.; Emsalem, M.; Gramain, F.; Huttner, M.; Langevin, M.; Laurent, M.; Mignotte, M.; Moreau, J.-C.; Philippon, P.; Reyssat, E.; Waldschmidt, M. 1 1984 ...and 41 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 564 Authors 37 Waldschmidt, Michel 18 Bugeaud, Yann 17 Dubickas, Artūras 15 Roy, Damien 14 Marques, Diego 10 Masser, David William 9 Mignotte, Maurice 9 Philippon, Patrice 7 Ably, Mohammed 7 Diaz, Guy 7 Fischler, Stéphane 7 Harbourne, Brian 7 Hirata-Kohno, Noriko 7 Laurent, Michel 7 Le, Maohua 7 Sha, Min 6 Adamczewski, Boris 6 Pethő, Attila 6 Rivoal, Tanguy 6 Tubbs, Robert 5 Chalebgwa, Taboka Prince 5 Corvaja, Pietro 5 David, Sinnou 5 Gaudron, Éric 5 Gramain, Francois 5 Luca, Florian 5 Moreira, Carlos Gustavo Tamm de Araujo 5 Murty, Maruti Ram 5 Stewart, Cameron L. 5 Yu, Kunrui 4 Berenstein, Carlos Alberto 4 Bertrand, Daniel 4 Bradley, David M. 4 Escassut, Alain 4 Levesque, Claude 4 Manchon, Dominique 4 Nakamaye, Michael 4 Pila, Jonathan 4 Rayaguru, Sai Gopal 4 Schleischitz, Johannes 4 Seceleanu, Alexandra 4 Shorey, Tarlok Nath 4 Szemberg, Tomasz 4 Tzanakis, Nikos 4 Wüstholz, Gisbert 4 Zannier, Umberto M. 4 Zhu, Yaochen 3 Amoroso, Francesco Antonio 3 Balakrishnan, Jennifer S. 3 Bijlsma, Alex 3 Bosser, Vincent 3 Bouillot, Olivier 3 Bruinier, Jan Hendrik 3 Caveny, Deanna M. 3 Chirskiĭ, Vladimir Grigor’evich 3 Cooper, Susan Marie 3 de Weger, Benjamin M. M. 3 D’Hoker, Eric 3 Dumnicki, Marcin 3 Ebrahimi-Fard, Kurusch 3 Glass, Andrew M. W. 3 Gun, Sanoli 3 Habegger, Philipp 3 Kumar, K. Senthil 3 Lara Rodríguez, José Alejandro 3 Malara, Grzegorz 3 Mosunov, Anton S. 3 Pellarin, Federico 3 Ramirez, Josimar 3 Reyssat, Eric 3 Shmelev, Andrey A. 3 Simsek, Yilmaz 3 Szpond, Justyna 3 Tutaj-Gasińska, Halszka 3 Unterberger, Jérémie M. 3 Yger, Alain 3 Yu, Jing 3 Ziegler, Volker 2 Balasubramanian, Ramachandran 2 Barbagallo, María Laura 2 Bell, Jason P. 2 Berger, Arno 2 Bézivin, Jean-Paul 2 Bilu, Yuri F. 2 Bocci, Cristiano 2 Bowman, Douglas C. 2 Bravo, Jhon Jairo 2 Brown, Francis C. S. 2 Brownawell, W. Dale 2 Bundschuh, Peter 2 Castillo-Medina, Jaime 2 Chang, Chieh-Yu 2 Chapoton, Frédéric 2 Chistikov, Dmitry V. 2 Cijsouw, Pieter Leendert 2 Cresson, Jacky 2 Delaunay, Sandra 2 Dipasquale, Michael R. 2 Dogra, Netan 2 Drmota, Michael ...and 464 more Authors all top 5 Cited in 158 Serials 64 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 13 Bulletin de la Société Mathématique de France 12 Bulletin of the Australian Mathematical Society 12 Mathematical Notes 12 Inventiones Mathematicae 12 Monatshefte für Mathematik 12 International Journal of Number Theory 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Advances in Mathematics 9 The Ramanujan Journal 8 Mathematics of Computation 8 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 8 Acta Mathematica Hungarica 8 Indagationes Mathematicae. New Series 7 Acta Arithmetica 7 Duke Mathematical Journal 7 Journal of Pure and Applied Algebra 7 Mathematische Annalen 7 Transactions of the American Mathematical Society 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 Archiv der Mathematik 5 Manuscripta Mathematica 4 Communications in Mathematical Physics 4 Israel Journal of Mathematics 4 Journal d’Analyse Mathématique 4 Journal of Algebra 4 Mémoires de la Société Mathématique de France. Nouvelle Série 4 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Zeitschrift 3 Rendiconti del Seminario Matematico della Università di Padova 3 Results in Mathematics 3 Journal of Symbolic Computation 3 Journal of the Ramanujan Mathematical Society 3 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 3 Linear Algebra and its Applications 3 Bulletin of the American Mathematical Society. New Series 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Acta Mathematica Sinica. New Series 3 Journal of Mathematical Sciences (New York) 3 Documenta Mathematica 3 Annals of Mathematics. Second Series 3 Journal of the European Mathematical Society (JEMS) 3 Journal of High Energy Physics 3 Integers 3 Journal of the Australian Mathematical Society 3 European Journal of Mathematics 2 Lithuanian Mathematical Journal 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 The Mathematical Intelligencer 2 Applied Mathematics and Computation 2 Canadian Mathematical Bulletin 2 Journal of Soviet Mathematics 2 Nagoya Mathematical Journal 2 Proceedings of the London Mathematical Society. Third Series 2 Theoretical Computer Science 2 Revista Matemática Iberoamericana 2 L’Enseignement Mathématique. 2e 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 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Doklady Mathematics 2 Logical Methods in Computer Science 2 Moscow Journal of Combinatorics and Number Theory 2 Research in Number Theory 2 Transactions of the American Mathematical Society. Series B 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Computer Physics Communications 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Nuclear Physics. B 1 Periodica Mathematica Hungarica 1 Physica A 1 Journal of Geometry and Physics 1 Acta Mathematica Vietnamica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Canadian Journal of Mathematics 1 Czechoslovak Mathematical Journal 1 Dissertationes Mathematicae 1 Functiones et Approximatio. Commentarii Mathematici 1 Glasgow Mathematical Journal 1 Publications Mathématiques 1 Integral Equations and Operator Theory 1 Journal of Combinatorial Theory. Series A ...and 58 more Serials all top 5 Cited in 50 Fields 484 Number theory (11-XX) 97 Algebraic geometry (14-XX) 51 Functions of a complex variable (30-XX) 35 Special functions (33-XX) 27 Commutative algebra (13-XX) 23 Several complex variables and analytic spaces (32-XX) 22 Dynamical systems and ergodic theory (37-XX) 19 Computer science (68-XX) 17 Combinatorics (05-XX) 17 Field theory and polynomials (12-XX) 12 Quantum theory (81-XX) 10 Mathematical logic and foundations (03-XX) 8 Approximations and expansions (41-XX) 7 History and biography (01-XX) 7 Group theory and generalizations (20-XX) 7 Ordinary differential equations (34-XX) 7 Manifolds and cell complexes (57-XX) 6 Associative rings and algebras (16-XX) 6 Difference and functional equations (39-XX) 6 Convex and discrete geometry (52-XX) 6 Probability theory and stochastic processes (60-XX) 5 Topological groups, Lie groups (22-XX) 5 Measure and integration (28-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Numerical analysis (65-XX) 4 Nonassociative rings and algebras (17-XX) 4 Real functions (26-XX) 4 Differential geometry (53-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistics (62-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Partial differential equations (35-XX) 2 Abstract harmonic analysis (43-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Operations research, mathematical programming (90-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 Sequences, series, summability (40-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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