Edit Profile (opens in new tab) Mazur, Barry Co-Author Distance Author ID: mazur.barry Published as: Mazur, Barry; Mazur, B.; Mazur, B. C. more...less Further Spellings: Mazur, Barry Charles; Мазур Барри Homepage: https://people.math.harvard.edu/~mazur/ External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Awards: Chern Medal (2022) Documents Indexed: 145 Publications since 1959, including 9 Books 23 Contributions as Editor · 7 Further Contributions Biographic References: 4 Publications Co-Authors: 102 Co-Authors with 105 Joint Publications 2,625 Co-Co-Authors all top 5 Co-Authors 65 single-authored 24 Rubin, Karl Cooper 14 Jerison, David S. 14 Schmid, Wilfried 14 Yau, Shing-Tung 10 Tate, John Torrence jun. 9 Mrowka, Tomasz S. 9 Stanley, Richard Peter 7 Artin, Michael 7 Harris, Joseph Daniel 5 Gouvêa, Fernando Quadros 4 Lusztig, George 4 Stein, William A. 3 Caporaso, Lucia 3 Coates, John Henry 3 de Jong, Aise Johan 3 Friedlander, Eric Mark 3 Graber, Tom 3 Klagsbrun, Zev 3 Ribet, Kenneth Alan 3 Serre, Jean-Pierre 3 Starr, Jason Michael 3 Wiles, Andrew John 2 Atiyah, Michael Francis 2 Boston, Nigel 2 Cremona, John E. 2 Friedlander, John Benjamin 2 Goldfeld, Dorian Morris 2 Gross, Benedict Hyman 2 Hirzebruch, Friedrich 2 Iwaniec, Henryk 2 Jackson, Allyn 2 Kamienny, Sheldon 2 Lax, Peter David 2 Lichtenbaum, Stephen 2 Messing, William 2 Singer, Isadore Manuel 2 Soulé, Christophe 2 Stroock, Daniel W. 1 Acquista, Karen 1 Adem, Alejandro 1 Agashe, Amod 1 Ardila, Federico 1 Arnol’d, Vladimir Igorevich 1 Ash, Avner 1 Baker, Matthew H. 1 Bass, Hyman 1 Bektemirov, Baur 1 Bonato, Anthony 1 Brown, Ken 1 Buhler, Joe P. 1 Burge, Tyler 1 Calegari, Frank 1 Chaitin, Gregory John 1 Chayes, Jennifer Tour 1 Chudnovsky, Maria 1 Chung, Fan 1 Çiperiani, Mirela 1 Clausen, Dustin 1 Clemens, C. Herbert 1 Coleman, Robert Frederick 1 Conlon, Lawrence 1 Cuntz, Joachim 1 Curtis, Edward B. 1 Daubechies, Ingrid Chantal 1 Dennett, Daniel C. 1 Derickx, Maarten 1 Doria, Francisco Antonio 1 Doxiadis, Apostolos 1 Duesberg, Peter 1 Duflot, Jeanne 1 Dwork, Bernard 1 Edwards, Harold Mortimer jun. 1 Eisenbud, David 1 Ewing, John Harwood 1 Føllesdal, Dagfinn 1 Fontaine, Jean-Marc 1 Gawȩdzki, Krzysztof 1 Gerver, Joseph L. 1 Ghoussoub, Nassif A. 1 Gillet, Henri A. 1 Gleason, Andrew Mattei 1 Goldberg, Lisa A. 1 Granville, Andrew James 1 Grayson, Daniel Richard 1 Greenberg, Marvin Jay 1 Greenberg, Ralph 1 Herman, Richard H. 1 Hirsch, Morris W. 1 Howe, Roger Evans 1 Huebschmann, Johannes 1 Humphrey, Nicholas 1 Jaffe, Arthur Michael 1 Jeffrey, Lisa Claire 1 Jorgenson, Jay Alan 1 Katz, Nicholas Michael 1 Kazhdan, David A. 1 Khare, Chandrashekhar 1 Kobayashi, Shoshichi 1 Kollár, János 1 Kramer, Jürg ...and 52 more Co-Authors all top 5 Serials 11 Inventiones Mathematicae 9 Bulletin of the American Mathematical Society. New Series 9 Annals of Mathematics. Second Series 8 Notices of the American Mathematical Society 7 Publications Mathématiques 4 Compositio Mathematica 4 Duke Mathematical Journal 3 American Journal of Mathematics 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Bulletin of the American Mathematical Society 3 Lecture Notes in Mathematics 2 Mathematics of Computation 2 The Mathematical Intelligencer 2 Annales de l’Institut Fourier 2 Illinois Journal of Mathematics 2 Journal für die Reine und Angewandte Mathematik 2 Memoirs of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Journal of the American Mathematical Society 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Documenta Mathematica 2 Annals of Mathematics Studies 1 American Mathematical Monthly 1 Acta Mathematica 1 Advances in Mathematics 1 Bulletin of the London Mathematical Society 1 Collectanea Mathematica 1 Journal of Algebra 1 Journal of Differential Geometry 1 The Journal of Symbolic Logic 1 Synthese 1 Topology 1 Proceedings of the National Academy of Sciences of the United States of America 1 Mathematical Research Letters 1 Izvestiya: Mathematics 1 European Mathematical Society Newsletter 1 The Asian Journal of Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Advanced Studies in Pure Mathematics 1 Contemporary Mathematics 1 Mathematicians of Our Time 1 Annales Mathématiques du Québec 1 ICCM Notices 1 Research in the Mathematical Sciences 1 Proceedings of the American Mathematical Society. Series B 1 The Frontiers Collection 1 Tunisian Journal of Mathematics all top 5 Fields 99 Number theory (11-XX) 79 Algebraic geometry (14-XX) 26 General and overarching topics; collections (00-XX) 21 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 4 Manifolds and cell complexes (57-XX) 3 Algebraic topology (55-XX) 2 Group theory and generalizations (20-XX) 2 Partial differential equations (35-XX) 2 Differential geometry (53-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 131 Publications have been cited 4,266 times in 3,105 Documents Cited by ▼ Year ▼ Modular curves and the Eisenstein ideal. Zbl 0394.14008Mazur, B. 430 1977 Rational isogenies of prime degree. (With an appendix by D. Goldfeld). Zbl 0386.14009Mazur, B. 316 1978 Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 277 1985 Class fields of abelian extensions of \(\mathbb Q\). Zbl 0545.12005Mazur, B.; Wiles, A. 231 1984 Rational points of Abelian varieties with values in towers of number fields. Zbl 0245.14015Mazur, Barry 213 1972 Etale homotopy. Zbl 0182.26001Artin, M.; Mazur, B. 193 1969 On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028Mazur, B.; Tate, J.; Teitelbaum, J. 190 1986 Arithmetic of Weil curves. Zbl 0281.14016Mazur, B.; Swinnerton-Dyer, P. 140 1974 On periodic points. Zbl 0127.13401Artin, M.; Mazur, B. 121 1965 Universal extensions and one dimensional crystalline cohomology. Zbl 0301.14016Mazur, Barry; Messing, William 86 1974 The eigencurve. Zbl 0932.11030Coleman, R.; Mazur, B. 71 1998 An introduction to the deformation theory of Galois representations. Zbl 0901.11015Mazur, Barry 71 1997 Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur. Zbl 0433.14032Gross, Benedict H. 68 1980 Deforming Galois representations. Zbl 0714.11076Mazur, B. 65 1989 Kolyvagin systems. Zbl 1055.11041Mazur, Barry; Rubin, Karl 60 2004 A note on some contractible 4-manifolds. Zbl 0127.13604Mazur, B. 59 1961 Geometric Galois representations. Zbl 0839.14011Fontaine, Jean-Marc; Mazur, Barry 57 1995 On \(p\)-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008Mazur, B.; Wiles, A. 55 1986 Formal groups arising from algebraic varieties. Zbl 0351.14023Artin, M.; Mazur, B. 54 1977 Frobenius and the Hodge filtration. Zbl 0258.14006Mazur, B. 53 1972 The square-free sieve and the rank of elliptic curves. Zbl 0725.11027Gouvêa, F.; Mazur, B. 52 1991 Uniformity of rational points. Zbl 0872.14017Caporaso, Lucia; Harris, Joe; Mazur, Barry 51 1997 Ranks of twists of elliptic curves and Hilbert’s tenth problem. Zbl 1227.11075Mazur, B.; Rubin, K. 49 2010 Smoothings of piecewise linear manifolds. Zbl 0298.57007Hirsch, Morris W.; Mazur, Barry 48 1974 Frobenius and the Hodge filtration (estimates). Zbl 0261.14005Mazur, B. 44 1973 Filtrations on the homology of algebraic varieties. Zbl 0841.14019Friedlander, Eric M.; Mazur, Barry 41 1994 Arithmetic on curves. Zbl 0593.14021Mazur, Barry 41 1986 On the arithmetic of special values of L functions. Zbl 0426.14009Mazur, B. 39 1979 Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004Mazur, B.; Tate, J. 38 1987 Galois representations, Kähler differentials and “main conjectures”. (Représentations galoisiennes, différentielles de Kähler et “conjectures principales”.) Zbl 0744.11053Mazur, B.; Tilouine, J. 37 1990 The topology of rational points. Zbl 0784.14012Mazur, Barry 37 1992 Finding large Selmer rank via an arithmetic theory of local constants. Zbl 1219.11084Mazur, Barry; Rubin, Karl 36 2007 On embeddings of spheres. Zbl 0086.37004Mazur, Barry 36 1959 Notes on etale cohomology of number fields. Zbl 0282.14004Mazur, Barry 33 1973 Canonical height pairings via biextensions. Zbl 0574.14036Mazur, B.; Tate, J. 33 1983 Rational points on modular curves. Zbl 0357.14005Mazur, B. 31 1977 Families of modular eigenforms. Zbl 0773.11030Gouvêa, F.; Mazur, B. 31 1992 Questions of decidability and undecidability in number theory. Zbl 0814.11059Mazur, B. 29 1994 On the van Kampen theorem. Zbl 0138.18301Artin, M.; Mazur, B. 29 1966 Local Euler characteristics. Zbl 0191.19202Mazur, B.; Roberts, L. 29 1970 Visualizing elements in the Shafarevich-Tate group. Zbl 0972.11049Cremona, John E.; Mazur, Barry 27 2000 Modular curves and arithmetic. Zbl 0597.14023Mazur, B. 25 1984 Points of order 13 on elliptic curves. Zbl 0268.14009Mazur, B.; Tate, J. 24 1973 Courbes elliptiques et symboles modulaires. Zbl 0276.14012Mazur, Barry 23 1973 The \(p\)-adic sigma function. Zbl 0735.14020Mazur, B.; Tate, J. 23 1991 Disparity in Selmer ranks of quadratic twists of elliptic curves. Zbl 1300.11063Klagsbrun, Zev; Mazur, Barry; Rubin, Karl 22 2013 Twisting commutative algebraic groups. Zbl 1128.14034Mazur, B.; Rubin, K.; Silverberg, A. 22 2007 Hypersurfaces of low degree. Zbl 0991.14018Harris, Joe; Mazur, Barry; Pandharipande, Rahul 22 1998 Evolutions, symbolic squares, and Fitting ideals. Zbl 0912.13010Eisenbud, David; Mazur, Barry 21 1997 Nearly ordinary Galois deformations over arbitrary number fields. Zbl 1211.11065Calegari, Frank; Mazur, Barry 21 2009 Rational torsion of prime order in elliptic curves over number fields (with an appendix by A. Granville). Zbl 0846.14012Kamienny, S.; Mazur, B. 20 1995 Two-dimensional representations in the arithmetic of modular curves. Zbl 0780.14015Mazur, B.; Ribet, K. A. 19 1991 Computation of \(p\)-adic heights and log convergence. Zbl 1135.11034Mazur, Barry; Stein, William; Tate, John 18 2007 Finding meaning in error terms. Zbl 1229.11001Mazur, Barry 18 2008 Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark 18 2007 Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero. With an Appendix by J. Cremona and B. Mazur. Zbl 1084.11033Agashe, Amod; Stein, William 17 2005 Relative neighborhoods and the theorems of Smale. Zbl 0112.38301Mazur, B. 17 1963 Differential topology from the point of view of simple homotopy theory. Zbl 0173.51203Mazur, Barry 15 1963 Number theory as gadfly. Zbl 0764.11021Mazur, B. 14 1991 Relative modular symbols and Rankin-Selberg convolutions. Zbl 0941.11020Kazhdan, D.; Mazur, B.; Schmidt, C.-G. 14 2000 Diophantine stability. Zbl 1491.14036Mazur, Barry; Rubin, Karl 14 2018 The spin of prime ideals. Zbl 1296.11150Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K. 13 2013 Local flat duality. Zbl 0199.24501Mazur, B. 13 1970 On the passage from local to global in number theory. Zbl 0813.14016Mazur, B. 13 1993 On monodromy invariants occurring in global arithmetic, and Fontaine’s theory. Zbl 0846.11039Mazur, B. 12 1994 Explicit universal deformations of Galois representations. Zbl 0739.11021Boston, N.; Mazur, B. 11 1989 Rational connectivity and sections of families over curves. Zbl 1092.14062Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason 11 2005 The method of infinite repetition in pure topology. I. Zbl 0133.16506Mazur, B. 11 1964 Speculations about the topology of rational points: An up-date. Zbl 0851.14009Mazur, B. 10 1995 How many rational points can a curve have? Zbl 0862.14012Caporaso, Lucia; Harris, Joe; Mazur, Barry 10 1995 An “infinite fern” in the universal deformation space of Galois representations. Zbl 0865.11046Mazur, B. 10 1997 Open problems regarding rational points on curves and varieties. Zbl 0943.14009Mazur, B. 10 1998 Mathematics: frontiers and perspectives. Zbl 1047.00015 10 2000 The theme of \(p\)-adic variation. Zbl 0959.14008Mazur, Barry 10 2000 Analogies between function fields and number fields. Zbl 0531.12015Mazur, B.; Wiles, A. 10 1983 Controlling Selmer groups in the higher core rank case. Zbl 1411.11065Mazur, Barry; Rubin, Karl 9 2016 On the characteristic power series of the \(U\) operator. Zbl 0779.11022Gouvêa, F. Q.; Mazur, B. 9 1993 Elliptic curves and class field theory. Zbl 1036.11023Mazur, Barry; Rubin, Karl 8 2002 Courbes de Weil de conducteur 26. Zbl 0241.14015Mazur, Barry; Velu, Jacques 8 1972 A Markov model for Selmer ranks in families of twists. Zbl 1316.11045Klagsbrun, Zev; Mazur, Barry; Rubin, Karl 8 2014 On the density of modular representations. Zbl 1134.11324Gouvêa, Fernando Q.; Mazur, Barry 8 1998 Perturbations, deformations, and variations (and “near-misses”) in geometry, physics, and number theory. Zbl 1057.11033Mazur, B. 8 2004 Refined class number formulas and Kolyvagin systems. Zbl 1225.11144Mazur, Barry; Rubin, Karl 7 2011 Two-dimensional \(p\)-adic Galois representations unramified away from \(p\). Zbl 0773.11036Mazur, B. 7 1990 Growth of Selmer rank in nonabelian extensions of number fields. Zbl 1151.11023Mazur, Barry; Rubin, Karl 7 2008 Refined class number formulas for \(\mathbb{G}_m\). Zbl 1414.11155Mazur, Barry; Rubin, Karl 7 2016 Abelian varieties and the Mordell-Lang conjecture. Zbl 0990.14006Mazur, Barry 7 2000 Rational families of \(17\)-torsion points of elliptic curves over number fields. Zbl 1440.11092Derickx, Maarten; Mazur, Barry; Kamienny, Sheldon 7 2018 How can we construct abelian Galois extensions of basic number fields? Zbl 1228.11163Mazur, Barry 6 2011 Questions about powers of numbers. Zbl 1041.11065Mazur, Barry 6 2000 Studying the growth of Mordell-Weil. Zbl 1142.11339Mazur, Barry; Rubin, Karl 6 2003 Organizing the arithmetic of elliptic curves. Zbl 1122.11038Mazur, Barry; Rubin, Karl 6 2005 Correspondence homomorphisms for singular varieties. Zbl 0811.14007Friedlander, Eric M.; Mazur, Barry 5 1994 Open problems: descending cohomology, geometrically. Zbl 1317.11004Mazur, Barry 5 2014 Visualizing elements of order three in the Shafarevich-Tate group. Zbl 0958.11043Mazur, B. 5 1999 On embeddings of spheres. Zbl 0096.37904Mazur, B. C. 5 1961 Eigenvalues of Frobenius acting on algebraic varieties over finite fields. Zbl 0306.14011Mazur, B. 4 1975 Circles disturbed. The interplay of mathematics and narrative. Zbl 1237.00022 4 2012 Symmetric homology spheres. Zbl 0103.39503Mazur, Barry 4 1962 Points rationnels des courbes modulaires \(X_0(N)\). Zbl 0346.14013Mazur, Barry; Serre, Jean-Pierre 3 1976 Notes for a seminar in axiomatic reasoning. Zbl 07632999Mazur, Barry 1 2022 Diophantine stability. Zbl 1491.14036Mazur, Barry; Rubin, Karl 14 2018 Rational families of \(17\)-torsion points of elliptic curves over number fields. Zbl 1440.11092Derickx, Maarten; Mazur, Barry; Kamienny, Sheldon 7 2018 Controlling Selmer groups in the higher core rank case. Zbl 1411.11065Mazur, Barry; Rubin, Karl 9 2016 Refined class number formulas for \(\mathbb{G}_m\). Zbl 1414.11155Mazur, Barry; Rubin, Karl 7 2016 Prime numbers and the Riemann hypothesis. Zbl 1356.11001Mazur, Barry; Stein, William 1 2016 A celebration of the mathematical work of Glenn Stevens. Zbl 1354.11004Mazur, Barry 1 2016 Alexandre Grothendieck 1928–2014, part 2. Zbl 1338.01023Ladegaillerie, Yves; Lichtenbaum, Stephen; Lochak, Pierre; Mazur, Barry; Messing, William; Murre, Jacob; Schneps, Leila 1 2016 Selmer companion curves. Zbl 1316.11047Mazur, Barry; Rubin, Karl 3 2015 Erratum to: “The spin of prime ideals”. Zbl 1330.11072Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K. 2 2015 A Markov model for Selmer ranks in families of twists. Zbl 1316.11045Klagsbrun, Zev; Mazur, Barry; Rubin, Karl 8 2014 Open problems: descending cohomology, geometrically. Zbl 1317.11004Mazur, Barry 5 2014 Is it plausible? Zbl 1307.11003Mazur, Barry 1 2014 Disparity in Selmer ranks of quadratic twists of elliptic curves. Zbl 1300.11063Klagsbrun, Zev; Mazur, Barry; Rubin, Karl 22 2013 The spin of prime ideals. Zbl 1296.11150Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K. 13 2013 Circles disturbed. The interplay of mathematics and narrative. Zbl 1237.00022 4 2012 Refined class number formulas and Kolyvagin systems. Zbl 1225.11144Mazur, Barry; Rubin, Karl 7 2011 How can we construct abelian Galois extensions of basic number fields? Zbl 1228.11163Mazur, Barry 6 2011 Ranks of twists of elliptic curves and Hilbert’s tenth problem. Zbl 1227.11075Mazur, B.; Rubin, K. 49 2010 Nearly ordinary Galois deformations over arbitrary number fields. Zbl 1211.11065Calegari, Frank; Mazur, Barry 21 2009 Finding meaning in error terms. Zbl 1229.11001Mazur, Barry 18 2008 Growth of Selmer rank in nonabelian extensions of number fields. Zbl 1151.11023Mazur, Barry; Rubin, Karl 7 2008 Current developments in mathematics, 2006. Zbl 1149.00018 1 2008 Mathematical Platonism and its opposites. Zbl 1154.00310Mazur, Barry 1 2008 Finding large Selmer rank via an arithmetic theory of local constants. Zbl 1219.11084Mazur, Barry; Rubin, Karl 36 2007 Twisting commutative algebraic groups. Zbl 1128.14034Mazur, B.; Rubin, K.; Silverberg, A. 22 2007 Computation of \(p\)-adic heights and log convergence. Zbl 1135.11034Mazur, Barry; Stein, William; Tate, John 18 2007 Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark 18 2007 Fearless symmetry. Exposing the hidden patterns of numbers. With a foreword by Barry Mazur. Zbl 1111.11001Ash, Avner; Gross, Robert 1 2006 Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero. With an Appendix by J. Cremona and B. Mazur. Zbl 1084.11033Agashe, Amod; Stein, William 17 2005 Rational connectivity and sections of families over curves. Zbl 1092.14062Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason 11 2005 Organizing the arithmetic of elliptic curves. Zbl 1122.11038Mazur, Barry; Rubin, Karl 6 2005 Finding large Selmer groups. Zbl 1211.11068Mazur, Barry; Rubin, Karl 3 2005 Kolyvagin systems. Zbl 1055.11041Mazur, Barry; Rubin, Karl 60 2004 Perturbations, deformations, and variations (and “near-misses”) in geometry, physics, and number theory. Zbl 1057.11033Mazur, B. 8 2004 Arithmetic questions related to rationally connected varieties. Zbl 1071.14053Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason 3 2004 Jumps in Mordell-Weil rank and arithmetic surjectivity. Zbl 1075.14021Graber, Tom; Harris, Joseph; Mazur, Barry; Starr, Jason 2 2004 Pairings in the arithmetic of elliptic curves. Zbl 1071.11028Mazur, Barry; Rubin, Karl 2 2004 What is …a motive? Zbl 1054.14511Mazur, Barry 1 2004 Studying the growth of Mordell-Weil. Zbl 1142.11339Mazur, Barry; Rubin, Karl 6 2003 Current developments in mathematics, 2003. Zbl 1090.00008 1 2003 Imagining numbers. Particularly the square root of minus fifteen. Zbl 1049.00502Mazur, Barry 1 2003 Elliptic curves and class field theory. Zbl 1036.11023Mazur, Barry; Rubin, Karl 8 2002 Reading Bombelli. Zbl 1023.01005La Nave, Federica; Mazur, Barry 2 2002 Current developments in mathematics 2000. Zbl 0990.00013 1 2001 Visualizing elements in the Shafarevich-Tate group. Zbl 0972.11049Cremona, John E.; Mazur, Barry 27 2000 Relative modular symbols and Rankin-Selberg convolutions. Zbl 0941.11020Kazhdan, D.; Mazur, B.; Schmidt, C.-G. 14 2000 Mathematics: frontiers and perspectives. Zbl 1047.00015 10 2000 The theme of \(p\)-adic variation. Zbl 0959.14008Mazur, Barry 10 2000 Abelian varieties and the Mordell-Lang conjecture. Zbl 0990.14006Mazur, Barry 7 2000 Questions about powers of numbers. Zbl 1041.11065Mazur, Barry 6 2000 Visualizing elements of order three in the Shafarevich-Tate group. Zbl 0958.11043Mazur, B. 5 1999 The eigencurve. Zbl 0932.11030Coleman, R.; Mazur, B. 71 1998 Hypersurfaces of low degree. Zbl 0991.14018Harris, Joe; Mazur, Barry; Pandharipande, Rahul 22 1998 Open problems regarding rational points on curves and varieties. Zbl 0943.14009Mazur, B. 10 1998 On the density of modular representations. Zbl 1134.11324Gouvêa, Fernando Q.; Mazur, Barry 8 1998 An introduction to the deformation theory of Galois representations. Zbl 0901.11015Mazur, Barry 71 1997 Uniformity of rational points. Zbl 0872.14017Caporaso, Lucia; Harris, Joe; Mazur, Barry 51 1997 Evolutions, symbolic squares, and Fitting ideals. Zbl 0912.13010Eisenbud, David; Mazur, Barry 21 1997 An “infinite fern” in the universal deformation space of Galois representations. Zbl 0865.11046Mazur, B. 10 1997 Conjecture. Zbl 1052.00513Mazur, B. 2 1997 Geometric Galois representations. Zbl 0839.14011Fontaine, Jean-Marc; Mazur, Barry 57 1995 Rational torsion of prime order in elliptic curves over number fields (with an appendix by A. Granville). Zbl 0846.14012Kamienny, S.; Mazur, B. 20 1995 Speculations about the topology of rational points: An up-date. Zbl 0851.14009Mazur, B. 10 1995 How many rational points can a curve have? Zbl 0862.14012Caporaso, Lucia; Harris, Joe; Mazur, Barry 10 1995 Searching for \(p\)-adic eigenfunctions. Zbl 0851.11031Gouvêa, Fernando Q.; Mazur, Barry 3 1995 Fermat’s last theorem. A lecture presented in Vancouver, British Columbia, Canada, August 1993. Videotape (NTSC). Zbl 0974.11500Mazur, Barry 1 1995 Filtrations on the homology of algebraic varieties. Zbl 0841.14019Friedlander, Eric M.; Mazur, Barry 41 1994 Questions of decidability and undecidability in number theory. Zbl 0814.11059Mazur, B. 29 1994 On monodromy invariants occurring in global arithmetic, and Fontaine’s theory. Zbl 0846.11039Mazur, B. 12 1994 Correspondence homomorphisms for singular varieties. Zbl 0811.14007Friedlander, Eric M.; Mazur, Barry 5 1994 On the passage from local to global in number theory. Zbl 0813.14016Mazur, B. 13 1993 On the characteristic power series of the \(U\) operator. Zbl 0779.11022Gouvêa, F. Q.; Mazur, B. 9 1993 The topology of rational points. Zbl 0784.14012Mazur, Barry 37 1992 Families of modular eigenforms. Zbl 0773.11030Gouvêa, F.; Mazur, B. 31 1992 The square-free sieve and the rank of elliptic curves. Zbl 0725.11027Gouvêa, F.; Mazur, B. 52 1991 The \(p\)-adic sigma function. Zbl 0735.14020Mazur, B.; Tate, J. 23 1991 Two-dimensional representations in the arithmetic of modular curves. Zbl 0780.14015Mazur, B.; Ribet, K. A. 19 1991 Number theory as gadfly. Zbl 0764.11021Mazur, B. 14 1991 A note on a classical theorem of Blichfeldt. Zbl 0746.52021Gillet, H.; Mazur, B.; Soulé, C. 3 1991 Galois representations, Kähler differentials and “main conjectures”. (Représentations galoisiennes, différentielles de Kähler et “conjectures principales”.) Zbl 0744.11053Mazur, B.; Tilouine, J. 37 1990 Two-dimensional \(p\)-adic Galois representations unramified away from \(p\). Zbl 0773.11036Mazur, B. 7 1990 Deforming Galois representations. Zbl 0714.11076Mazur, B. 65 1989 Explicit universal deformations of Galois representations. Zbl 0739.11021Boston, N.; Mazur, B. 11 1989 Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004Mazur, B.; Tate, J. 38 1987 On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028Mazur, B.; Tate, J.; Teitelbaum, J. 190 1986 On \(p\)-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008Mazur, B.; Wiles, A. 55 1986 Arithmetic on curves. Zbl 0593.14021Mazur, Barry 41 1986 Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 277 1985 Class fields of abelian extensions of \(\mathbb Q\). Zbl 0545.12005Mazur, B.; Wiles, A. 231 1984 Modular curves and arithmetic. Zbl 0597.14023Mazur, B. 25 1984 Canonical height pairings via biextensions. Zbl 0574.14036Mazur, B.; Tate, J. 33 1983 Analogies between function fields and number fields. Zbl 0531.12015Mazur, B.; Wiles, A. 10 1983 Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur. Zbl 0433.14032Gross, Benedict H. 68 1980 On the arithmetic of special values of L functions. Zbl 0426.14009Mazur, B. 39 1979 Rational isogenies of prime degree. (With an appendix by D. Goldfeld). Zbl 0386.14009Mazur, B. 316 1978 Collected papers. Vol. III: Topology of curves and surfaces, and special topics in the theory of algebraic varieties. Edited and with an introduction by M. Artin and B. Mazur. Zbl 0446.14001Zariski, Oscar 3 1978 Modular curves and the Eisenstein ideal. Zbl 0394.14008Mazur, B. 430 1977 Formal groups arising from algebraic varieties. Zbl 0351.14023Artin, M.; Mazur, B. 54 1977 Rational points on modular curves. Zbl 0357.14005Mazur, B. 31 1977 ...and 31 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,410 Authors 45 Mazur, Barry 30 Lei, Antonio 23 Hida, Haruzo 23 Rubin, Karl Cooper 19 Lim, Meng Fai 18 Büyükboduk, Kâzim 18 Najman, Filip 18 Shlapentokh, Alexandra 17 Ray, Anwesh 16 Bleher, Frauke M. 16 Darmon, Henri René 15 Kamienny, Sheldon 14 Bertolini, Massimo 13 Dummigan, Neil 13 Friedlander, Eric Mark 13 González-Jiménez, Enrique 12 Balakrishnan, Jennifer S. 12 Castella, Francesc 12 Ichimura, Humio 12 Siksek, Samir 11 Bandini, Andrea 11 Chen, Imin 11 Dujella, Andrej 11 Khare, Chandrashekhar 11 Longhi, Ignazio 11 Lozano-Robledo, Álvaro 11 Perrin-Riou, Bernadette 11 Porter, Timothy 11 Ribet, Kenneth Alan 10 Böckle, Gebhard 10 Calegari, Frank 10 Chinburg, Ted 10 Jeon, Daeyeol 10 Kurihara, Masato 10 Ochiai, Tadashi 10 Pasten, Hector V. 10 Tilouine, Jacques 10 Yoo, Hwajong 9 Burungale, Ashay A. 9 Byeon, Dongho 9 Clark, Peter Louis 9 Emerton, Matthew 9 Gee, Toby 9 Gross, Benedict Hyman 9 Harris, Michael Howard 9 Klosin, Krzysztof 9 Longo, Matteo 9 Panchishkin, Alexei A. 9 Poonen, Bjorn 9 Stoll, Michael 9 Trihan, Fabien 9 Vâjâitu, Marian 9 Voight, John Michael 9 Wiles, Andrew John 8 Bellaïche, Joël 8 Bennett, Michael A. 8 Buium, Alexandru 8 Coleman, Robert Frederick 8 Conrad, Brian 8 Delbourgo, Daniel 8 Greenberg, Ralph 8 Greither, Cornelius 8 Murty, Maruti Ram 8 Rotger, Victor 8 Silverberg, Alice 8 Skinner, Christopher M. 8 Stein, William A. 8 Ramdorai, Sujatha 8 Tan, Ki-Seng 8 Tornero, José María 8 Vatsal, Vinayak 8 Vigni, Stefano 8 Zaharescu, Alexandru 8 Zarkhin, Yuriĭ Gennad’evich 7 Achter, Jeffrey D. 7 Agashe, Amod 7 Barrios, Alexander J. 7 Betina, Adel 7 Bley, Werner 7 Byszewski, Jakub 7 Cegarra, Antonio Martínez 7 Cornelissen, Gunther 7 Daniels, Harris B. 7 Derickx, Maarten 7 Dieulefait, Luis Victor 7 Fisher, Tom A. 7 Kato, Kazuya 7 Kim, Byoung Du 7 Kundu, Debanjana 7 Momose, Fumiyuki 7 Ono, Ken 7 Pál, Ambrus 7 Papikian, Mihran 7 Seveso, Marco Adamo 7 Tamagawa, Akio 7 Taylor, Richard Lawrence 7 Urban, Eric 7 Vélez-Marulanda, José A. 7 Wake, Preston 7 Wan, Daqing ...and 2,310 more Authors all top 5 Cited in 282 Serials 291 Journal of Number Theory 156 Inventiones Mathematicae 128 Transactions of the American Mathematical Society 115 Compositio Mathematica 96 Duke Mathematical Journal 94 Mathematische Annalen 77 International Journal of Number Theory 76 Journal de Théorie des Nombres de Bordeaux 71 Journal of Algebra 67 Annales de l’Institut Fourier 65 Journal of Pure and Applied Algebra 60 Advances in Mathematics 58 Proceedings of the American Mathematical Society 56 Mathematische Zeitschrift 48 Journal für die Reine und Angewandte Mathematik 47 Bulletin of the American Mathematical Society. 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Académie des Sciences, Paris 17 Annales Mathématiques du Québec 17 Research in the Mathematical Sciences 16 Rocky Mountain Journal of Mathematics 15 Communications in Algebra 15 Bulletin de la Société Mathématique de France 14 Nagoya Mathematical Journal 13 Archiv der Mathematik 13 Bulletin of the London Mathematical Society 12 Cahiers de Topologie et Géométrie Différentielle Catégoriques 12 Memoirs of the American Mathematical Society 12 Journal of Algebraic Geometry 11 Journal of Soviet Mathematics 11 Pacific Journal of Mathematics 11 Publications of the Research Institute for Mathematical Sciences, Kyoto University 11 Tokyo Journal of Mathematics 11 Ergodic Theory and Dynamical Systems 10 Bulletin of the Australian Mathematical Society 10 Functiones et Approximatio. Commentarii Mathematici 10 Journal of the Ramanujan Mathematical Society 10 Selecta Mathematica. New Series 10 Geometry & Topology 9 Proceedings of the London Mathematical Society. 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New Series 5 Doklady Mathematics 5 Advances in Geometry ...and 182 more Serials all top 5 Cited in 54 Fields 2,095 Number theory (11-XX) 1,259 Algebraic geometry (14-XX) 197 Algebraic topology (55-XX) 164 Manifolds and cell complexes (57-XX) 134 Category theory; homological algebra (18-XX) 123 Dynamical systems and ergodic theory (37-XX) 113 Group theory and generalizations (20-XX) 88 Commutative algebra (13-XX) 74 \(K\)-theory (19-XX) 58 Several complex variables and analytic spaces (32-XX) 52 Topological groups, Lie groups (22-XX) 51 Associative rings and algebras (16-XX) 46 Mathematical logic and foundations (03-XX) 46 Field theory and polynomials (12-XX) 40 Global analysis, analysis on manifolds (58-XX) 38 Differential geometry (53-XX) 32 General topology (54-XX) 26 Combinatorics (05-XX) 22 History and biography (01-XX) 22 Functions of a complex variable (30-XX) 20 Convex and discrete geometry (52-XX) 20 Quantum theory (81-XX) 16 General and overarching topics; collections (00-XX) 14 Nonassociative rings and algebras (17-XX) 12 Geometry (51-XX) 12 Computer science (68-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Functional analysis (46-XX) 10 Information and communication theory, circuits (94-XX) 9 Measure and integration (28-XX) 7 Partial differential equations (35-XX) 6 Special functions (33-XX) 6 Ordinary differential equations (34-XX) 6 Operator theory (47-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Real functions (26-XX) 5 Difference and functional equations (39-XX) 4 Numerical analysis (65-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistics (62-XX) 3 Relativity and gravitational theory (83-XX) 3 Biology and other natural sciences (92-XX) 2 Potential theory (31-XX) 2 Approximations and expansions (41-XX) 2 Abstract harmonic analysis (43-XX) 2 Mechanics of particles and systems (70-XX) 2 Systems theory; control (93-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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