Edit Profile (opens in new tab) Christol, Gilles Co-Author Distance Author ID: christol.gilles Published as: Christol, Gilles; Christol, G. Homepage: https://webusers.imj-prg.fr/~gilles.christol/ External Links: MGP · Wikidata · dblp · IdRef · theses.fr Member of Collective: Parent, D. P. Documents Indexed: 59 Publications since 1968, including 6 Books 13 Contributions as Editor · 1 Further Contribution Reviewing Activity: 102 Reviews Co-Authors: 21 Co-Authors with 37 Joint Publications 314 Co-Co-Authors all top 5 Co-Authors 35 single-authored 14 Robba, Philippe 13 Amice, Yvette 9 Mebkhout, Zoghman 3 Bostan, Alin 3 Dwork, Bernard Morris 2 Cot, Anne 2 Dumas, Philippe 2 Marle, Charles-Michel 2 Pilibossian, Philippe 2 Yammine, Sleiman 1 Boukraa, Salah 1 Caruso, Xavier 1 Chiarellotto, Bruno 1 de Fermat, Pierre 1 Hassani, Saoud 1 Houzel, Christian 1 Kamae, Teturo 1 Loeser, François 1 Maillard, Jean-Marie 1 Mendès France, Michel 1 Rashed, Roshdi 1 Rauzy, Gerard 1 Remmal, Salah-eddine 1 Schikhof, Wilhelmus Hendricus all top 5 Serials 2 Annales de l’Institut Fourier 2 Bulletin de la Société Mathématique de France 2 Gazette des Mathématiciens 2 Séminaire d’Analyse. Université Blaise Pascal. Clermont II 2 Annals of Mathematics. Second Series 1 Compositio Mathematica 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Pacific Journal of Mathematics 1 Theoretical Computer Science 1 Annales Mathématiques Blaise Pascal 1 European Mathematical Society Newsletter 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Queen’s Papers in Pure and Applied Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Collection Sciences dans l’Histoire all top 5 Fields 48 Field theory and polynomials (12-XX) 37 Number theory (11-XX) 19 Algebraic geometry (14-XX) 17 General and overarching topics; collections (00-XX) 13 Ordinary differential equations (34-XX) 10 Commutative algebra (13-XX) 6 Computer science (68-XX) 3 Functional analysis (46-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Operator theory (47-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 41 Publications have been cited 502 times in 300 Documents Cited by ▼ Year ▼ Suites algébriques, automates et substitutions. Zbl 0472.10035Christol, G.; Kamae, T.; Mendès France, Michel; Rauzy, Gérard 158 1980 Ensembles presque périodiques \(k\)-reconnaissables. (Almost periodic \(k\)-recognizable sets). Zbl 0402.68044Christol, Gilles 67 1979 On the index theorem for \(p\)-adic differential equations. III. (Sur le théorème de l’indice des équations différentielles \(p\)-adiques. III.) Zbl 1078.12500Christol, G.; Mebkhout, Z. 28 2000 Modules différentiels sur les couronnes (Differential modules over annuli). Zbl 0859.12004Christol, Gilles; Dwork, Bernard 27 1994 On the index theorem for \(p\)-adic differential equations. IV. (Sur le théorème de l’indice des équations différentielles \(p\)-adiques. IV.) Zbl 1078.12501Christol, G.; Mebkhout, Z. 27 2001 On the index theorem for \(p\)-adic differential equations. II. (Sur le théorème de l’indice des équations différentielles \(p\)-adiques. II.) Zbl 0929.12003Christol, G.; Mebkhout, Z. 21 1997 Differential modules and \(p\)-adic differential equations. (Modules différentiels et équations différentielles \(p\)-adiques.) Zbl 0589.12020Christol, Gilles 20 1983 Ising \(n\)-fold integrals as diagonals of rational functions and integrality of series expansions. Zbl 1267.82021Bostan, A.; Boukraa, S.; Christol, G.; Hassani, S.; Maillard, J.-M. 18 2013 \(p\)-adic differential equations. Applications to exponential sums. (Equations différentielles \(p\)-adiques. Applications aux sommes exponentielles.) Zbl 0868.12006Robba, Philippe; Christol, Gilles 16 1994 Un théorème de transfert pour les discques singuliers réguliers. Zbl 0553.12014Christol, Gilles 14 1984 Effective \(p\)-adic bounds at regular singular points. Zbl 0762.12004Christol, G.; Dwork, B. 11 1991 On the index theorem for \(p\)-adic differential equations. I. (Sur le théorème de l’indice des équations différentielles \(p\)- adiques. I.) Zbl 0834.12005Christol, G.; Mebkhout, Z. 11 1993 Fonctions et éléments algébriques. (Algebraic functions and elements). Zbl 0591.12018Christol, Gilles 9 1986 Équations différentielles \(p\)-adiques et coefficients \(p\)-adiques sur les courbes. (\(p\)-adic differential equations and \(p\)-adic coefficients over curves). Zbl 1031.12004Christol, Gilles; Mebkhout, Zoghman 9 2002 Solutions algébriques des équations différentielles \(p\)-adiques. Zbl 0525.12020Christol, G. 7 1983 Diagonales de fractions rationnelles et équations différentielles. Zbl 0534.12018Christol, Gilles 7 1984 Systèmes différentiels linéaires \(p\)-adiques, structure de Frobenius faible. Zbl 0459.12020Christol, Gilles 5 1981 Diagonals of rational fractions. Zbl 1380.12006Christol, Gilles 5 2015 On overconvergent isocrystals and \(F\)-isocrystals of rank one. Zbl 0934.12004Chiarellotto, Bruno; Christol, Gilles 5 1996 Diagonales de fractions rationelles. (Diagonals of rational fractions). Zbl 0694.13013Christol, Gilles 4 1988 Differential modules of bounded spectral norm. Zbl 0765.12003Christol, G.; Dwork, B. 3 1992 Globally bounded solutions of differential equations. Zbl 0705.12006Christol, Gilles 3 1990 The radius of convergence function for first order differential equations. Zbl 1238.12006Christol, Gilles 3 2011 Éléments analytiques uniformes et multiformes. Zbl 0328.12013Christol, Gilles 3 1975 Groupe d’étude d’analyse ultramétrique. 13ème année: 1985/86. Zbl 0649.00010 2 1986 Fast computation of the \(N\)th term of an algebraic series over a finite prime field. Zbl 1364.12009Bostan, Alin; Christol, Gilles; Dumas, Philippe 2 2016 Décomposition des matrices en facteurs singuliers applications aux équations différentielles. Zbl 0466.12016Christol, Gilles 2 1981 Sur une opération analogue à l’opération de Cartier en caractéristique nulle. Zbl 0194.34803Christol, G. 2 1970 Irregular \(p\)-adic linear differential equations. Zbl 0994.12001Remmal, S.; Christol, G. 2 2000 Opération de Cartier et vecteurs de Witt. Zbl 0272.14004Christol, Gilles 1 1972 \(p\)-adic numbers and ultrametricity. Zbl 0809.11076Christol, Gilles 1 1992 Topological \(p\)-adic vector spaces and index theory. Zbl 0838.47054Christol, Gilles; Mebkhout, Zoghman 1 1995 About a Tsuzuki theorem. Zbl 0986.14012Christol, G. 1 2001 An application of \(c\)-compactness. Zbl 1053.46055Christol, G.; Mebkhout, Z.; Schikhof, W. H. 1 1999 Works of Pierre Fermat. I: Number theory. Translated by Paul Tannery. With an introduction and commentary by R. Rashed, Ch. Houzel and G. Christol. (Œuvres de Pierre Fermat. I: La théorie des nombres.) Zbl 0961.01035Fermat, Pierre 1 1999 Thirty years later. Zbl 1095.12003Christol, Gilles 1 2004 Erratum à “Diagonale de fractions rationnelles”. (Erratum to: “Diagonals of rational fractions”). Zbl 0698.13009Christol, G. 1 1990 Structure de Frobenius différentielles p-adiques. Zbl 0352.12015Christol, Gilles 1 1977 \(p\)-adic differential equations. Zbl 0994.12002Christol, G.; Mebkhout, Z. 1 2000 Study group on ultrametric analysis. 10th year: 1982/83. No. 1. (Groupe d’étude d’analyse ultramétrique. 10ème année: 1982/83. Fasc. 1.) Zbl 1489.12010 1 1984 Study group on ultrametric analysis. 11th year: 1983/84. (Groupe d’étude d’analyse ultramétrique. 11ème année: 1983/84.) Zbl 1489.12012 1 1985 Fast computation of the \(N\)th term of an algebraic series over a finite prime field. Zbl 1364.12009Bostan, Alin; Christol, Gilles; Dumas, Philippe 2 2016 Diagonals of rational fractions. Zbl 1380.12006Christol, Gilles 5 2015 Ising \(n\)-fold integrals as diagonals of rational functions and integrality of series expansions. Zbl 1267.82021Bostan, A.; Boukraa, S.; Christol, G.; Hassani, S.; Maillard, J.-M. 18 2013 The radius of convergence function for first order differential equations. Zbl 1238.12006Christol, Gilles 3 2011 Thirty years later. Zbl 1095.12003Christol, Gilles 1 2004 Équations différentielles \(p\)-adiques et coefficients \(p\)-adiques sur les courbes. (\(p\)-adic differential equations and \(p\)-adic coefficients over curves). Zbl 1031.12004Christol, Gilles; Mebkhout, Zoghman 9 2002 On the index theorem for \(p\)-adic differential equations. IV. (Sur le théorème de l’indice des équations différentielles \(p\)-adiques. IV.) Zbl 1078.12501Christol, G.; Mebkhout, Z. 27 2001 About a Tsuzuki theorem. Zbl 0986.14012Christol, G. 1 2001 On the index theorem for \(p\)-adic differential equations. III. (Sur le théorème de l’indice des équations différentielles \(p\)-adiques. III.) Zbl 1078.12500Christol, G.; Mebkhout, Z. 28 2000 Irregular \(p\)-adic linear differential equations. Zbl 0994.12001Remmal, S.; Christol, G. 2 2000 \(p\)-adic differential equations. Zbl 0994.12002Christol, G.; Mebkhout, Z. 1 2000 An application of \(c\)-compactness. Zbl 1053.46055Christol, G.; Mebkhout, Z.; Schikhof, W. H. 1 1999 Works of Pierre Fermat. I: Number theory. Translated by Paul Tannery. With an introduction and commentary by R. Rashed, Ch. Houzel and G. Christol. (Œuvres de Pierre Fermat. I: La théorie des nombres.) Zbl 0961.01035Fermat, Pierre 1 1999 On the index theorem for \(p\)-adic differential equations. II. (Sur le théorème de l’indice des équations différentielles \(p\)-adiques. II.) Zbl 0929.12003Christol, G.; Mebkhout, Z. 21 1997 On overconvergent isocrystals and \(F\)-isocrystals of rank one. Zbl 0934.12004Chiarellotto, Bruno; Christol, Gilles 5 1996 Topological \(p\)-adic vector spaces and index theory. Zbl 0838.47054Christol, Gilles; Mebkhout, Zoghman 1 1995 Modules différentiels sur les couronnes (Differential modules over annuli). Zbl 0859.12004Christol, Gilles; Dwork, Bernard 27 1994 \(p\)-adic differential equations. Applications to exponential sums. (Equations différentielles \(p\)-adiques. Applications aux sommes exponentielles.) Zbl 0868.12006Robba, Philippe; Christol, Gilles 16 1994 On the index theorem for \(p\)-adic differential equations. I. (Sur le théorème de l’indice des équations différentielles \(p\)- adiques. I.) Zbl 0834.12005Christol, G.; Mebkhout, Z. 11 1993 Differential modules of bounded spectral norm. Zbl 0765.12003Christol, G.; Dwork, B. 3 1992 \(p\)-adic numbers and ultrametricity. Zbl 0809.11076Christol, Gilles 1 1992 Effective \(p\)-adic bounds at regular singular points. Zbl 0762.12004Christol, G.; Dwork, B. 11 1991 Globally bounded solutions of differential equations. Zbl 0705.12006Christol, Gilles 3 1990 Erratum à “Diagonale de fractions rationnelles”. (Erratum to: “Diagonals of rational fractions”). Zbl 0698.13009Christol, G. 1 1990 Diagonales de fractions rationelles. (Diagonals of rational fractions). Zbl 0694.13013Christol, Gilles 4 1988 Fonctions et éléments algébriques. (Algebraic functions and elements). Zbl 0591.12018Christol, Gilles 9 1986 Groupe d’étude d’analyse ultramétrique. 13ème année: 1985/86. Zbl 0649.00010 2 1986 Study group on ultrametric analysis. 11th year: 1983/84. (Groupe d’étude d’analyse ultramétrique. 11ème année: 1983/84.) Zbl 1489.12012 1 1985 Un théorème de transfert pour les discques singuliers réguliers. Zbl 0553.12014Christol, Gilles 14 1984 Diagonales de fractions rationnelles et équations différentielles. Zbl 0534.12018Christol, Gilles 7 1984 Study group on ultrametric analysis. 10th year: 1982/83. No. 1. (Groupe d’étude d’analyse ultramétrique. 10ème année: 1982/83. Fasc. 1.) Zbl 1489.12010 1 1984 Differential modules and \(p\)-adic differential equations. (Modules différentiels et équations différentielles \(p\)-adiques.) Zbl 0589.12020Christol, Gilles 20 1983 Solutions algébriques des équations différentielles \(p\)-adiques. Zbl 0525.12020Christol, G. 7 1983 Systèmes différentiels linéaires \(p\)-adiques, structure de Frobenius faible. Zbl 0459.12020Christol, Gilles 5 1981 Décomposition des matrices en facteurs singuliers applications aux équations différentielles. Zbl 0466.12016Christol, Gilles 2 1981 Suites algébriques, automates et substitutions. Zbl 0472.10035Christol, G.; Kamae, T.; Mendès France, Michel; Rauzy, Gérard 158 1980 Ensembles presque périodiques \(k\)-reconnaissables. (Almost periodic \(k\)-recognizable sets). Zbl 0402.68044Christol, Gilles 67 1979 Structure de Frobenius différentielles p-adiques. Zbl 0352.12015Christol, Gilles 1 1977 Éléments analytiques uniformes et multiformes. Zbl 0328.12013Christol, Gilles 3 1975 Opération de Cartier et vecteurs de Witt. Zbl 0272.14004Christol, Gilles 1 1972 Sur une opération analogue à l’opération de Cartier en caractéristique nulle. Zbl 0194.34803Christol, G. 2 1970 all cited Publications top 5 cited Publications all top 5 Cited by 248 Authors 25 Allouche, Jean-Paul Simon 11 Kedlaya, Kiran Sridhara 10 Shallit, Jeffrey Outlaw 9 Mendès France, Michel 8 Bell, Jason P. 8 Christol, Gilles 8 Wen, Zhixiong 6 Chiarellotto, Bruno 6 Hu, Yining 6 Mebkhout, Zoghman 6 Yao, Jiayan 5 Bostan, Alin 5 Maillard, Jean-Marie 5 Nakagawa, Takahiro 5 Skordev, Gencho S. 5 Tsuzuki, Nobuo 5 van der Poorten, Alfred J. 5 Yassawi, Reem 4 Abe, Tomoyuki 4 Barbé, André M. 4 Caro, Daniel 4 Dumas, Philippe 4 Dwork, Bernard Morris 4 Guo, Yingjun 4 Koutschan, Christoph 4 Moshe, Yossi 4 Peitgen, Heinz-Otto 4 Pulita, Andrea 4 Rowland, Eric S. 4 von Haeseler, Fritz 4 Wen, Zhiying 4 Winterhof, Arne 3 Abdelaziz, Y. 3 Adamczewski, Boris 3 André, Yves 3 Baldassarri, Francesco 3 Boukraa, Salah 3 Coons, Michael 3 Dekking, Frederik Michel 3 Durand, Fabien 3 Han, Guo-Niu 3 Lasjaunias, Alain 3 Manjra, Said 3 Mauduit, Christian 3 Mérai, László 3 Perez-Garcia, Cristina 3 Salvy, Bruno 3 Scheicher, Klaus 3 Tapsoba, Théodore Marie-Yves 3 Ulas, Maciej 3 Yurkevich, Sergey V. 2 Azzouz, Tinhinane A. 2 Bézivin, Jean-Paul 2 Bousquet-Mélou, Mireille 2 Bruyère, Véronique 2 Byszewski, Jakub 2 Černý, Anton 2 Crew, Richard M. 2 Drmota, Michael 2 Dumont, Jean-Marie 2 Hansel, Georges 2 Harase, Takashi 2 Kamae, Teturo 2 Klurman, Oleksiy 2 Kochubeĭ, Anatoliĭ Naumovych 2 Konieczny, Jakub 2 Kurlberg, Pär 2 Lemańczyk, Mariusz 2 Lipshitz, Leonard 2 Melczer, Stephen 2 Mkaouar, Mohamed 2 Peyrière, Jacques 2 Popoli, Pierre 2 Queffelec, Martine 2 Rampersad, Narad 2 Rauzy, Gerard 2 Remmal, Salah-eddine 2 Rivoal, Tanguy 2 Robba, Philippe 2 Salon, Olivier 2 Sharif, Habib 2 Shiho, Atsushi 2 Stoll, Thomas 2 Straub, Armin 2 Thakur, Dinesh S. 2 Thomas, Alain 2 Xiao, Liang 2 Zhang, Jiemeng 2 Żmija, Błażej 1 Abbes, Farah 1 Ablinger, Jakob 1 Agrawal, Shishir 1 Albayrak, Seda 1 Allombert, Bill 1 Anderson, Greg W. 1 Andriamampianina, D. Razafy 1 Arabia, Alberto 1 Bakinova, Ekaterina 1 Banderier, Cyril 1 Baranwal, Aseem R. ...and 148 more Authors all top 5 Cited in 101 Serials 32 Theoretical Computer Science 20 Journal of Number Theory 17 Journal de Théorie des Nombres de Bordeaux 12 Annales de l’Institut Fourier 12 Bulletin de la Société Mathématique de France 8 Journal of Algebra 8 Rendiconti del Seminario Matematico della Università di Padova 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Mathematische Annalen 6 Compositio Mathematica 5 Discrete Mathematics 5 Duke Mathematical Journal 5 Inventiones Mathematicae 5 Mathematische Zeitschrift 5 Advances in Applied Mathematics 5 RAIRO. Informatique Théorique et Applications 5 Journal of the Institute of Mathematics of Jussieu 5 Journal of Physics A: Mathematical and Theoretical 4 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 4 Finite Fields and their Applications 4 International Journal of Number Theory 3 Israel Journal of Mathematics 3 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 3 Documenta Mathematica 3 Cryptography and Communications 3 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 2 Discrete Applied Mathematics 2 The Mathematical Intelligencer 2 Advances in Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Journal of Combinatorial Theory. Series A 2 Transactions of the American Mathematical Society 2 Journal of Symbolic Computation 2 Mémoires de la Société Mathématique de France. Nouvelle Série 2 Annales Mathématiques Blaise Pascal 2 The Ramanujan Journal 2 Actes des Rencontres du C.I.R.M. 1 Bulletin of the Australian Mathematical Society 1 Information Processing Letters 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 Beiträge zur Algebra und Geometrie 1 Acta Arithmetica 1 Acta Mathematica 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Computation 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Journal of Functional Analysis 1 Journal of the Korean Mathematical Society 1 Journal of Pure and Applied Algebra 1 The Journal of Symbolic Logic 1 Manuscripta Mathematica 1 Mathematica Slovaca 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 RAIRO, Informatique Théorique 1 Tôhoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 European Journal of Combinatorics 1 Combinatorica 1 Acta Mathematica Hungarica 1 Probability Theory and Related Fields 1 Information and Computation 1 Journal of the American Mathematical Society 1 Discrete Mathematics and Applications 1 Linear Algebra and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Journal of Knot Theory and its Ramifications 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Experimental Mathematics 1 Combinatorics, Probability and Computing 1 Kyushu Journal of Mathematics 1 Selecta Mathematica. New Series 1 Bulletin des Sciences Mathématiques 1 Journal of Difference Equations and Applications 1 Theory of Computing Systems 1 Journal of Integer Sequences 1 Annals of Mathematics. Second Series 1 LMS Journal of Computation and Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 RAIRO. Theoretical Informatics and Applications 1 Integers 1 Foundations of Computational Mathematics 1 Frontiers of Mathematics in China 1 Algebra & Number Theory 1 Uniform Distribution Theory 1 RAIRO. Theoretical Informatics and Applications 1 Sahand Communications in Mathematical Analysis 1 Research in Number Theory 1 Algebraic Structures and their Applications ...and 1 more Serials all top 5 Cited in 37 Fields 182 Number theory (11-XX) 96 Computer science (68-XX) 68 Field theory and polynomials (12-XX) 67 Algebraic geometry (14-XX) 32 Commutative algebra (13-XX) 20 Combinatorics (05-XX) 14 Special functions (33-XX) 14 Dynamical systems and ergodic theory (37-XX) 9 Ordinary differential equations (34-XX) 7 Associative rings and algebras (16-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Operator theory (47-XX) 6 Group theory and generalizations (20-XX) 6 Functional analysis (46-XX) 4 Mathematical logic and foundations (03-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Measure and integration (28-XX) 3 Functions of a complex variable (30-XX) 3 Approximations and expansions (41-XX) 2 General and overarching topics; collections (00-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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