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## Wiles, Andrew John

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 Author ID: wiles.andrew-j Published as: Wiles, Andrew; Wiles, A.; Wiles, Andrew J.; Wiles, A. J. Homepage: https://www.maths.ox.ac.uk/people/andrew.wiles External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef Awards: Wolf Prize (1996) · Clay Research Award (1999) · Shaw Prize (2005) · Abel Prize (2016)
 Documents Indexed: 28 Publications since 1977, including 1 Book Biographic References: 15 Publications
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#### Co-Authors

 11 single-authored 4 Coates, John H. 4 Skinner, Christopher M. 3 Mazur, Barry 2 Snowden, Andrew W. 1 Carlson, James A. 1 Çiperiani, Mirela 1 Jaffe, Arthur Michael 1 Patrikis, Stefan T. 1 Rubin, Karl Cooper 1 Taylor, Richard Lawrence
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#### Serials

 6 Annals of Mathematics. Second Series 4 Inventiones Mathematicae 2 Duke Mathematical Journal 1 American Journal of Mathematics 1 Compositio Mathematica 1 Publications Mathématiques 1 Journal of the London Mathematical Society. Second Series 1 IMRN. International Mathematics Research Notices 1 Journal of the Australian Mathematical Society. Series A 1 Proceedings of the National Academy of Sciences of the United States of America 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI

#### Fields

 27 Number theory (11-XX) 10 Algebraic geometry (14-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX)

#### Citations contained in zbMATH Open

27 Publications have been cited 1,653 times in 1,040 Documents Cited by Year
Modular elliptic curves and Fermat’s Last Theorem. Zbl 0823.11029
Wiles, Andrew
1995
Ring-theoretic properties of certain Hecke algebras. Zbl 0823.11030
Taylor, Richard; Wiles, Andrew
1995
Class fields of abelian extensions of $$\mathbb Q$$. Zbl 0545.12005
Mazur, B.; Wiles, A.
1984
On ordinary $$\lambda$$-adic representations associated to modular forms. Zbl 0664.10013
Wiles, A.
1988
The Iwasawa conjecture for totally real fields. Zbl 0719.11071
Wiles, A.
1990
On the conjecture of Birch and Swinnerton-Dyer. Zbl 0359.14009
Coates, J.; Wiles, A.
1977
On $$p$$-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008
Mazur, B.; Wiles, A.
1986
Residually reducible representations and modular forms. Zbl 1005.11030
Skinner, C. M.; Wiles, A. J.
1999
Nearly ordinary deformations of irreducible residual representations. Zbl 1024.11036
Skinner, C. M.; Wiles, Andrew J.
2001
On $$p$$-adic $$L$$-functions and elliptic units. Zbl 0442.12007
Coates, J.; Wiles, A.
1978
Higher explicit reciprocity laws. Zbl 0378.12006
Wiles, A.
1978
On $$p$$-adic representations for totally real fields. Zbl 0613.12013
Wiles, A.
1986
Base change and a problem of Serre. Zbl 1016.11017
Skinner, C. M.; Wiles, A. J.
2001
Modular curves and the class group of $$\mathbb{Q} (\zeta_p)$$. Zbl 0436.12004
Wiles, Andrew
1980
The Millennium Prize problems. Zbl 1155.00001
Carlson, J. (ed.); Jaffe, A. (ed.); Wiles, A. (ed.)
2006
Kummer’s criterion for Hurwitz numbers. Zbl 0369.12009
Coates, J.; Wiles, A.
1977
On a conjecture of Brumer. Zbl 0719.11082
Wiles, A.
1990
Ordinary representations and modular forms. Zbl 0924.11044
Skinner, C. M.; Wiles, A. J.
1997
The Birch and Swinnerton-Dyer conjecture. Zbl 1194.11006
Wiles, Andrew
2006
Analogies between function fields and number fields. Zbl 0531.12015
Mazur, B.; Wiles, A.
1983
Solvable points on genus one curves. Zbl 1168.14014
Çiperiani, Mirela; Wiles, Andrew
2008
Mordell-Weil groups of elliptic curves over cyclotomic fields. Zbl 0519.14017
Rubin, Karl; Wiles, Andrew
1982
Bigness in compatible systems. Zbl 1407.11073
Snowden, Andrew; Wiles, Andrew
2016
On class groups of imaginary quadratic fields. Zbl 1387.11080
Wiles, A.
2015
Modular forms, elliptic curves, and Fermat’s Last Theorem. Zbl 0864.11029
Wiles, Andrew
1995
Explicit reciprocity laws. Zbl 0358.12001
Coates, J.; Wiles, A.
1977
Twenty years of number theory. Zbl 0965.11001
Wiles, Andrew
2000
Bigness in compatible systems. Zbl 1407.11073
Snowden, Andrew; Wiles, Andrew
2016
On class groups of imaginary quadratic fields. Zbl 1387.11080
Wiles, A.
2015
Solvable points on genus one curves. Zbl 1168.14014
Çiperiani, Mirela; Wiles, Andrew
2008
The Millennium Prize problems. Zbl 1155.00001
Carlson, J.; Jaffe, A.; Wiles, A.
2006
The Birch and Swinnerton-Dyer conjecture. Zbl 1194.11006
Wiles, Andrew
2006
Nearly ordinary deformations of irreducible residual representations. Zbl 1024.11036
Skinner, C. M.; Wiles, Andrew J.
2001
Base change and a problem of Serre. Zbl 1016.11017
Skinner, C. M.; Wiles, A. J.
2001
Twenty years of number theory. Zbl 0965.11001
Wiles, Andrew
2000
Residually reducible representations and modular forms. Zbl 1005.11030
Skinner, C. M.; Wiles, A. J.
1999
Ordinary representations and modular forms. Zbl 0924.11044
Skinner, C. M.; Wiles, A. J.
1997
Modular elliptic curves and Fermat’s Last Theorem. Zbl 0823.11029
Wiles, Andrew
1995
Ring-theoretic properties of certain Hecke algebras. Zbl 0823.11030
Taylor, Richard; Wiles, Andrew
1995
Modular forms, elliptic curves, and Fermat’s Last Theorem. Zbl 0864.11029
Wiles, Andrew
1995
The Iwasawa conjecture for totally real fields. Zbl 0719.11071
Wiles, A.
1990
On a conjecture of Brumer. Zbl 0719.11082
Wiles, A.
1990
On ordinary $$\lambda$$-adic representations associated to modular forms. Zbl 0664.10013
Wiles, A.
1988
On $$p$$-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008
Mazur, B.; Wiles, A.
1986
On $$p$$-adic representations for totally real fields. Zbl 0613.12013
Wiles, A.
1986
Class fields of abelian extensions of $$\mathbb Q$$. Zbl 0545.12005
Mazur, B.; Wiles, A.
1984
Analogies between function fields and number fields. Zbl 0531.12015
Mazur, B.; Wiles, A.
1983
Mordell-Weil groups of elliptic curves over cyclotomic fields. Zbl 0519.14017
Rubin, Karl; Wiles, Andrew
1982
Modular curves and the class group of $$\mathbb{Q} (\zeta_p)$$. Zbl 0436.12004
Wiles, Andrew
1980
On $$p$$-adic $$L$$-functions and elliptic units. Zbl 0442.12007
Coates, J.; Wiles, A.
1978
Higher explicit reciprocity laws. Zbl 0378.12006
Wiles, A.
1978
On the conjecture of Birch and Swinnerton-Dyer. Zbl 0359.14009
Coates, J.; Wiles, A.
1977
Kummer’s criterion for Hurwitz numbers. Zbl 0369.12009
Coates, J.; Wiles, A.
1977
Explicit reciprocity laws. Zbl 0358.12001
Coates, J.; Wiles, A.
1977
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#### Cited by 852 Authors

 17 Hida, Haruzo 13 Ichimura, Humio 12 Khare, Chandrashekhar 12 Rubin, Karl Cooper 11 Bennett, Michael A. 11 Siksek, Samir 11 Taylor, Richard Lawrence 10 Bleher, Frauke M. 10 Büyükboduk, Kâzim 10 Freitas, Nuno 10 Greither, Cornelius 10 Klosin, Krzysztof 10 Wiles, Andrew John 9 Calegari, Frank 9 Dieulefait, Luis Victor 9 Gee, Toby 9 Ochiai, Tadashi 9 Schimmrigk, Rolf 9 Virdol, Cristian 8 Darmon, Henri René 8 Kurihara, Masato 8 Mazur, Barry 8 Panchishkin, Alexei A. 8 Tilouine, Jacques 7 Berger, Tobias 7 Diamond, Fred 7 Dummigan, Neil 7 Lei, Antonio 7 Murty, Maruti Ram 7 Ozaki, Manabu 6 Böckle, Gebhard 6 Coates, John H. 6 Emerton, Matthew 6 Nguyen Quang Do, Thong 6 Rotger, Victor 6 Skinner, Christopher M. 6 Sumida-Takahashi, Hiroki 6 Thorne, Jack A. 6 Urban, Eric 6 Vatsal, Vinayak 5 Bandini, Andrea 5 Bars Cortina, Francesc 5 Bellaïche, Joël 5 Castella, Francesc 5 Chinburg, Ted 5 Coleman, Robert Frederick 5 Dąbrowski, Andrzej Bogdan 5 de Shalit, Ehud 5 Dimitrov, Mladen 5 Geraghty, David 5 Greenberg, Ralph 5 Guitart, Xavier 5 Harris, Michael Howard 5 Hsieh, Ming-Lun 5 Kakde, Mahesh 5 Kato, Kazuya 5 Longhi, Ignazio 5 Nickel, Andreas 5 Pollack, Robert 5 Ramdorai, Sujatha 5 Wang-Erickson, Carl 4 Anglès, Bruno 4 Aoki, Miho 4 Bertolini, Massimo 4 Browkin, Jerzy 4 Brown, Jim L. 4 Byeon, Dongho 4 Chen, Imin 4 Conrad, Brian 4 Dasgupta, Samit 4 Delaunay, Christophe 4 Gras, Georges 4 Kisin, Mark 4 Kolster, Manfred 4 Komatsu, Keiichi 4 Longo, Matteo 4 Newton, James 4 Pasten, Hector V. 4 Poonen, Bjorn 4 Popescu, Cristian D. 4 Rohrlich, David E. 4 Schoof, René 4 Sharifi, Romyar T. 4 Voight, John Michael 4 Wake, Preston 4 Wan, Xin 4 Weiss, Alfred R. 4 Xu, Hongyan 4 Yamagami, Atsushi 3 Betina, Adel 3 Bruinier, Jan Hendrik 3 Carbó-Dorca, Ramon 3 Çiperiani, Mirela 3 Dahmen, Sander R. 3 Delbourgo, Daniel 3 Dembélé, Lassina 3 Duncan, John F. R. 3 Fouquet, Olivier 3 Frey, Gerhard 3 Fukaya, Takako ...and 752 more Authors
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#### Cited in 187 Serials

 127 Journal of Number Theory 70 Inventiones Mathematicae 59 Compositio Mathematica 43 Duke Mathematical Journal 33 Mathematische Annalen 31 Annales de l’Institut Fourier 29 Journal de Théorie des Nombres de Bordeaux 26 International Journal of Number Theory 23 Transactions of the American Mathematical Society 20 Mathematics of Computation 20 Journal für die Reine und Angewandte Mathematik 19 Mathematische Zeitschrift 18 Journal of Algebra 18 Bulletin of the American Mathematical Society. New Series 14 Journal of the American Mathematical Society 13 Experimental Mathematics 12 Proceedings of the American Mathematical Society 10 Israel Journal of Mathematics 10 Mathematical Proceedings of the Cambridge Philosophical Society 10 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 10 Manuscripta Mathematica 9 Advances in Mathematics 9 Annales Mathématiques du Québec 9 Research in Number Theory 8 Functiones et Approximatio. Commentarii Mathematici 8 Proceedings of the Japan Academy. Series A 8 Annals of Mathematics. Second Series 7 Communications in Algebra 7 Acta Arithmetica 7 Bulletin de la Société Mathématique de France 7 Glasgow Mathematical Journal 7 Nagoya Mathematical Journal 7 Algebra & Number Theory 6 Bulletin of the Australian Mathematical Society 6 Tokyo Journal of Mathematics 6 Selecta Mathematica. New Series 6 The Ramanujan Journal 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of the Institute of Mathematics of Jussieu 6 Kyoto Journal of Mathematics 6 Forum of Mathematics, Sigma 6 Research in the Mathematical Sciences 5 Proceedings of the National Academy of Sciences of the United States of America 4 American Mathematical Monthly 4 Publications Mathématiques 4 Journal of the Mathematical Society of Japan 4 Journal of Pure and Applied Algebra 4 Osaka Journal of Mathematics 4 Proceedings of the London Mathematical Society. Third Series 4 Tohoku Mathematical Journal. Second Series 4 Journal of the Ramanujan Mathematical Society 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Journal of Algebraic Geometry 4 Journal of the European Mathematical Society (JEMS) 4 Acta Mathematica Sinica. English Series 3 International Journal of Modern Physics A 3 Nuclear Physics. B 3 Journal of the London Mathematical Society. Second Series 3 Journal of Soviet Mathematics 3 Mathematische Nachrichten 3 Mathematika 3 Revista Matemática Iberoamericana 3 International Journal of Mathematics 3 Elemente der Mathematik 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Mémoires de la Société Mathématique de France. Nouvelle Série 3 Journal of Mathematical Sciences (New York) 3 Journal of Mathematical Chemistry 3 Geometry & Topology 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Journal of Mathematical Analysis and Applications 2 Rocky Mountain Journal of Mathematics 2 Journal of Geometry and Physics 2 The Mathematical Intelligencer 2 Acta Mathematica Vietnamica 2 Archiv der Mathematik 2 Canadian Journal of Mathematics 2 Commentarii Mathematici Helvetici 2 Journal of Computational and Applied Mathematics 2 Kodai Mathematical Journal 2 Memoirs of the American Mathematical Society 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Theoretical Computer Science 2 Bulletin of the Korean Mathematical Society 2 Journal of Symbolic Computation 2 Indagationes Mathematicae. New Series 2 St. Petersburg Mathematical Journal 2 Finite Fields and their Applications 2 The Bulletin of Symbolic Logic 2 Documenta Mathematica 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 LMS Journal of Computation and Mathematics 2 Milan Journal of Mathematics 2 International Journal of Geometric Methods in Modern Physics 2 Mediterranean Journal of Mathematics 2 Japanese Journal of Mathematics. 3rd Series 1 Modern Physics Letters A 1 International Journal of Modern Physics B ...and 87 more Serials
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#### Cited in 44 Fields

 933 Number theory (11-XX) 255 Algebraic geometry (14-XX) 29 Group theory and generalizations (20-XX) 28 $$K$$-theory (19-XX) 21 Commutative algebra (13-XX) 19 Associative rings and algebras (16-XX) 13 History and biography (01-XX) 13 Mathematical logic and foundations (03-XX) 13 Quantum theory (81-XX) 12 Field theory and polynomials (12-XX) 12 Topological groups, Lie groups (22-XX) 11 Partial differential equations (35-XX) 10 Functions of a complex variable (30-XX) 9 General and overarching topics; collections (00-XX) 9 Several complex variables and analytic spaces (32-XX) 8 Manifolds and cell complexes (57-XX) 8 Computer science (68-XX) 7 Difference and functional equations (39-XX) 7 Fluid mechanics (76-XX) 7 Relativity and gravitational theory (83-XX) 7 Information and communication theory, circuits (94-XX) 6 Numerical analysis (65-XX) 5 Combinatorics (05-XX) 5 Ordinary differential equations (34-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Category theory; homological algebra (18-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Geometry (51-XX) 4 Probability theory and stochastic processes (60-XX) 3 Special functions (33-XX) 3 Mathematics education (97-XX) 2 Nonassociative rings and algebras (17-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX)

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