Edit Profile (opens in new tab) Mazur, Barry Compute Distance To: Compute 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: 143 Publications since 1959, including 9 Books 23 Contributions as Editor · 7 Further Contributions Biographic References: 2 Publications Co-Authors: 102 Co-Authors with 104 Joint Publications 2,554 Co-Co-Authors all top 5 Co-Authors 64 single-authored 23 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 H. 3 de Jong, Aise Johan 3 Friedlander, Eric Mark 3 Graber, Tom 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 Klagsbrun, Zev 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 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 51 more Co-Authors all top 5 Serials 11 Inventiones Mathematicae 9 Bulletin of the American Mathematical Society. New Series 8 Notices of the American Mathematical Society 8 Annals of Mathematics. Second Series 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 98 Number theory (11-XX) 78 Algebraic geometry (14-XX) 25 General and overarching topics; collections (00-XX) 20 History and biography (01-XX) 4 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) 2 Probability theory and stochastic processes (60-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-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 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 129 Publications have been cited 3,928 times in 2,805 Documents Cited by ▼ Year ▼ Modular curves and the Eisenstein ideal. Zbl 0394.14008Mazur, B. 380 1977 Rational isogenies of prime degree. (With an appendix by D. Goldfeld). Zbl 0386.14009Mazur, B. 283 1978 Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 251 1985 Class fields of abelian extensions of \(\mathbb Q\). Zbl 0545.12005Mazur, B.; Wiles, A. 223 1984 Rational points of Abelian varieties with values in towers of number fields. Zbl 0245.14015Mazur, Barry 195 1972 Etale homotopy. Zbl 0182.26001Artin, M.; Mazur, B. 175 1969 On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028Mazur, B.; Tate, J.; Teitelbaum, J. 171 1986 Arithmetic of Weil curves. Zbl 0281.14016Mazur, B.; Swinnerton-Dyer, P. 133 1974 On periodic points. Zbl 0127.13401Artin, M.; Mazur, B. 116 1965 Universal extensions and one dimensional crystalline cohomology. Zbl 0301.14016Mazur, Barry; Messing, William 79 1974 An introduction to the deformation theory of Galois representations. Zbl 0901.11015Mazur, Barry 62 1997 Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur. Zbl 0433.14032Gross, Benedict H. 60 1980 Deforming Galois representations. Zbl 0714.11076Mazur, B. 58 1989 Geometric Galois representations. Zbl 0839.14011Fontaine, Jean-Marc; Mazur, Barry 55 1995 On \(p\)-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008Mazur, B.; Wiles, A. 54 1986 The eigencurve. Zbl 0932.11030Coleman, R.; Mazur, B. 54 1998 A note on some contractible 4-manifolds. Zbl 0127.13604Mazur, B. 53 1961 Formal groups arising from algebraic varieties. Zbl 0351.14023Artin, M.; Mazur, B. 52 1977 The square-free sieve and the rank of elliptic curves. Zbl 0725.11027Gouvêa, F.; Mazur, B. 48 1991 Frobenius and the Hodge filtration. Zbl 0258.14006Mazur, B. 48 1972 Kolyvagin systems. Zbl 1055.11041Mazur, Barry; Rubin, Karl 45 2004 Smoothings of piecewise linear manifolds. Zbl 0298.57007Hirsch, Morris W.; Mazur, Barry 43 1974 Uniformity of rational points. Zbl 0872.14017Caporaso, Lucia; Harris, Joe; Mazur, Barry 43 1997 Frobenius and the Hodge filtration (estimates). Zbl 0261.14005Mazur, B. 41 1973 Ranks of twists of elliptic curves and Hilbert’s tenth problem. Zbl 1227.11075Mazur, B.; Rubin, K. 41 2010 Galois representations, Kähler differentials and “main conjectures”. (Représentations galoisiennes, différentielles de Kähler et “conjectures principales”.) Zbl 0744.11053Mazur, B.; Tilouine, J. 37 1990 On the arithmetic of special values of L functions. Zbl 0426.14009Mazur, B. 35 1979 The topology of rational points. Zbl 0784.14012Mazur, Barry 35 1992 Filtrations on the homology of algebraic varieties. Zbl 0841.14019Friedlander, Eric M.; Mazur, Barry 35 1994 Arithmetic on curves. Zbl 0593.14021Mazur, Barry 34 1986 Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004Mazur, B.; Tate, J. 34 1987 On embeddings of spheres. Zbl 0086.37004Mazur, Barry 32 1959 Canonical height pairings via biextensions. Zbl 0574.14036Mazur, B.; Tate, J. 31 1983 Finding large Selmer rank via an arithmetic theory of local constants. Zbl 1219.11084Mazur, Barry; Rubin, Karl 30 2007 Local Euler characteristics. Zbl 0191.19202Mazur, B.; Roberts, L. 29 1970 Notes on etale cohomology of number fields. Zbl 0282.14004Mazur, Barry 28 1973 Families of modular eigenforms. Zbl 0773.11030Gouvêa, F.; Mazur, B. 28 1992 Questions of decidability and undecidability in number theory. Zbl 0814.11059Mazur, B. 28 1994 Visualizing elements in the Shafarevich-Tate group. Zbl 0972.11049Cremona, John E.; Mazur, Barry 26 2000 On the van Kampen theorem. Zbl 0138.18301Artin, M.; Mazur, B. 26 1966 Rational points on modular curves. Zbl 0357.14005Mazur, B. 25 1977 Points of order 13 on elliptic curves. Zbl 0268.14009Mazur, B.; Tate, J. 24 1973 Modular curves and arithmetic. Zbl 0597.14023Mazur, B. 22 1984 Courbes elliptiques et symboles modulaires. Zbl 0276.14012Mazur, Barry 20 1973 Disparity in Selmer ranks of quadratic twists of elliptic curves. Zbl 1300.11063Klagsbrun, Zev; Mazur, Barry; Rubin, Karl 20 2013 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 Hypersurfaces of low degree. Zbl 0991.14018Harris, Joe; Mazur, Barry; Pandharipande, Rahul 19 1998 The \(p\)-adic sigma function. Zbl 0735.14020Mazur, B.; Tate, J. 19 1991 Nearly ordinary Galois deformations over arbitrary number fields. Zbl 1211.11065Calegari, Frank; Mazur, Barry 19 2009 Finding meaning in error terms. Zbl 1229.11001Mazur, Barry 18 2008 Evolutions, symbolic squares, and Fitting ideals. Zbl 0912.13010Eisenbud, David; Mazur, Barry 18 1997 Twisting commutative algebraic groups. Zbl 1128.14034Mazur, B.; Rubin, K.; Silverberg, A. 18 2007 Relative neighborhoods and the theorems of Smale. Zbl 0112.38301Mazur, B. 16 1963 Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark 15 2007 Computation of \(p\)-adic heights and log convergence. Zbl 1135.11034Mazur, Barry; Stein, William; Tate, John 15 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 15 2005 Two-dimensional representations in the arithmetic of modular curves. Zbl 0780.14015Mazur, B.; Ribet, K. A. 15 1991 Differential topology from the point of view of simple homotopy theory. Zbl 0173.51203Mazur, Barry 14 1963 Local flat duality. Zbl 0199.24501Mazur, B. 13 1970 Relative modular symbols and Rankin-Selberg convolutions. Zbl 0941.11020Kazhdan, D.; Mazur, B.; Schmidt, C.-G. 13 2000 On the passage from local to global in number theory. Zbl 0813.14016Mazur, B. 13 1993 Number theory as gadfly. Zbl 0764.11021Mazur, B. 12 1991 The spin of prime ideals. Zbl 1296.11150Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K. 11 2013 Explicit universal deformations of Galois representations. Zbl 0739.11021Boston, N.; Mazur, B. 11 1989 The method of infinite repetition in pure topology. I. Zbl 0133.16506Mazur, B. 11 1964 On monodromy invariants occurring in global arithmetic, and Fontaine’s theory. Zbl 0846.11039Mazur, B. 11 1994 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 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 Rational connectivity and sections of families over curves. Zbl 1092.14062Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason 9 2005 Analogies between function fields and number fields. Zbl 0531.12015Mazur, B.; Wiles, A. 9 1983 Controlling Selmer groups in the higher core rank case. Zbl 1411.11065Mazur, Barry; Rubin, Karl 8 2016 A Markov model for Selmer ranks in families of twists. Zbl 1316.11045Klagsbrun, Zev; Mazur, Barry; Rubin, Karl 7 2014 Courbes de Weil de conducteur 26. Zbl 0241.14015Mazur, Barry; Velu, Jacques 7 1972 Elliptic curves and class field theory. Zbl 1036.11023Mazur, Barry; Rubin, Karl 7 2002 An “infinite fern” in the universal deformation space of Galois representations. Zbl 0865.11046Mazur, B. 7 1997 Perturbations, deformations, and variations (and “near-misses”) in geometry, physics, and number theory. Zbl 1057.11033Mazur, B. 7 2004 Two-dimensional \(p\)-adic Galois representations unramified away from \(p\). Zbl 0773.11036Mazur, B. 7 1990 Refined class number formulas and Kolyvagin systems. Zbl 1225.11144Mazur, Barry; Rubin, Karl 7 2011 On the characteristic power series of the \(U\) operator. Zbl 0779.11022Gouvêa, F. Q.; Mazur, B. 7 1993 Refined class number formulas for \(\mathbb{G}_m\). Zbl 1414.11155Mazur, Barry; Rubin, Karl 6 2016 Growth of Selmer rank in nonabelian extensions of number fields. Zbl 1151.11023Mazur, Barry; Rubin, Karl 6 2008 On the density of modular representations. Zbl 1134.11324Gouvêa, Fernando Q.; Mazur, Barry 6 1998 Studying the growth of Mordell-Weil. Zbl 1142.11339Mazur, Barry; Rubin, Karl 6 2003 Diophantine stability. Zbl 06924832Mazur, Barry; Rubin, Karl 6 2018 Rational families of \(17\)-torsion points of elliptic curves over number fields. Zbl 1440.11092Derickx, Maarten; Mazur, Barry; Kamienny, Sheldon 6 2018 Visualizing elements of order three in the Shafarevich-Tate group. Zbl 0958.11043Mazur, B. 5 1999 Abelian varieties and the Mordell-Lang conjecture. Zbl 0990.14006Mazur, Barry 5 2000 Open problems: descending cohomology, geometrically. Zbl 1317.11004Mazur, Barry 5 2014 Organizing the arithmetic of elliptic curves. Zbl 1122.11038Mazur, Barry; Rubin, Karl 5 2005 Correspondence homomorphisms for singular varieties. Zbl 0811.14007Friedlander, Eric M.; Mazur, Barry 5 1994 Questions about powers of numbers. Zbl 1041.11065Mazur, Barry 5 2000 How can we construct abelian Galois extensions of basic number fields? Zbl 1228.11163Mazur, Barry 5 2011 Eigenvalues of Frobenius acting on algebraic varieties over finite fields. Zbl 0306.14011Mazur, B. 4 1975 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 4 1978 On embeddings of spheres. Zbl 0096.37904Mazur, B. C. 4 1961 Symmetric homology spheres. Zbl 0103.39503Mazur, Barry 4 1962 Homotopy of varieties in the etale topology. Zbl 0188.53402Artin, M.; Mazur, B. 3 1967 Diophantine stability. Zbl 06924832Mazur, Barry; Rubin, Karl 6 2018 Rational families of \(17\)-torsion points of elliptic curves over number fields. Zbl 1440.11092Derickx, Maarten; Mazur, Barry; Kamienny, Sheldon 6 2018 Controlling Selmer groups in the higher core rank case. Zbl 1411.11065Mazur, Barry; Rubin, Karl 8 2016 Refined class number formulas for \(\mathbb{G}_m\). Zbl 1414.11155Mazur, Barry; Rubin, Karl 6 2016 Prime numbers and the Riemann hypothesis. Zbl 1356.11001Mazur, Barry; Stein, William 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 A celebration of the mathematical work of Glenn Stevens. Zbl 1354.11004Mazur, Barry 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 7 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 20 2013 The spin of prime ideals. Zbl 1296.11150Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K. 11 2013 Circles disturbed. The interplay of mathematics and narrative. Zbl 1237.00022 1 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 5 2011 Ranks of twists of elliptic curves and Hilbert’s tenth problem. Zbl 1227.11075Mazur, B.; Rubin, K. 41 2010 Nearly ordinary Galois deformations over arbitrary number fields. Zbl 1211.11065Calegari, Frank; Mazur, Barry 19 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 6 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 30 2007 Twisting commutative algebraic groups. Zbl 1128.14034Mazur, B.; Rubin, K.; Silverberg, A. 18 2007 Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark 15 2007 Computation of \(p\)-adic heights and log convergence. Zbl 1135.11034Mazur, Barry; Stein, William; Tate, John 15 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 15 2005 Rational connectivity and sections of families over curves. Zbl 1092.14062Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason 9 2005 Organizing the arithmetic of elliptic curves. Zbl 1122.11038Mazur, Barry; Rubin, Karl 5 2005 Finding large Selmer groups. Zbl 1211.11068Mazur, Barry; Rubin, Karl 3 2005 Kolyvagin systems. Zbl 1055.11041Mazur, Barry; Rubin, Karl 45 2004 Perturbations, deformations, and variations (and “near-misses”) in geometry, physics, and number theory. Zbl 1057.11033Mazur, B. 7 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 What is …a motive? Zbl 1054.14511Mazur, Barry 1 2004 Pairings in the arithmetic of elliptic curves. Zbl 1071.11028Mazur, Barry; Rubin, Karl 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 7 2002 Reading Bombelli. Zbl 1023.01005La Nave, Federica; Mazur, Barry 2 2002 Visualizing elements in the Shafarevich-Tate group. Zbl 0972.11049Cremona, John E.; Mazur, Barry 26 2000 Relative modular symbols and Rankin-Selberg convolutions. Zbl 0941.11020Kazhdan, D.; Mazur, B.; Schmidt, C.-G. 13 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 5 2000 Questions about powers of numbers. Zbl 1041.11065Mazur, Barry 5 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. 54 1998 Hypersurfaces of low degree. Zbl 0991.14018Harris, Joe; Mazur, Barry; Pandharipande, Rahul 19 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 6 1998 An introduction to the deformation theory of Galois representations. Zbl 0901.11015Mazur, Barry 62 1997 Uniformity of rational points. Zbl 0872.14017Caporaso, Lucia; Harris, Joe; Mazur, Barry 43 1997 Evolutions, symbolic squares, and Fitting ideals. Zbl 0912.13010Eisenbud, David; Mazur, Barry 18 1997 An “infinite fern” in the universal deformation space of Galois representations. Zbl 0865.11046Mazur, B. 7 1997 Conjecture. Zbl 1052.00513Mazur, B. 2 1997 Geometric Galois representations. Zbl 0839.14011Fontaine, Jean-Marc; Mazur, Barry 55 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 35 1994 Questions of decidability and undecidability in number theory. Zbl 0814.11059Mazur, B. 28 1994 On monodromy invariants occurring in global arithmetic, and Fontaine’s theory. Zbl 0846.11039Mazur, B. 11 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. 7 1993 The topology of rational points. Zbl 0784.14012Mazur, Barry 35 1992 Families of modular eigenforms. Zbl 0773.11030Gouvêa, F.; Mazur, B. 28 1992 The square-free sieve and the rank of elliptic curves. Zbl 0725.11027Gouvêa, F.; Mazur, B. 48 1991 The \(p\)-adic sigma function. Zbl 0735.14020Mazur, B.; Tate, J. 19 1991 Two-dimensional representations in the arithmetic of modular curves. Zbl 0780.14015Mazur, B.; Ribet, K. A. 15 1991 Number theory as gadfly. Zbl 0764.11021Mazur, B. 12 1991 A note on a classical theorem of Blichfeldt. Zbl 0746.52021Gillet, H.; Mazur, B.; Soulé, C. 2 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. 58 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. 34 1987 On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028Mazur, B.; Tate, J.; Teitelbaum, J. 171 1986 On \(p\)-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008Mazur, B.; Wiles, A. 54 1986 Arithmetic on curves. Zbl 0593.14021Mazur, Barry 34 1986 Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 251 1985 Class fields of abelian extensions of \(\mathbb Q\). Zbl 0545.12005Mazur, B.; Wiles, A. 223 1984 Modular curves and arithmetic. Zbl 0597.14023Mazur, B. 22 1984 Canonical height pairings via biextensions. Zbl 0574.14036Mazur, B.; Tate, J. 31 1983 Analogies between function fields and number fields. Zbl 0531.12015Mazur, B.; Wiles, A. 9 1983 Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur. Zbl 0433.14032Gross, Benedict H. 60 1980 On the arithmetic of special values of L functions. Zbl 0426.14009Mazur, B. 35 1979 Rational isogenies of prime degree. (With an appendix by D. Goldfeld). Zbl 0386.14009Mazur, B. 283 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 4 1978 Modular curves and the Eisenstein ideal. Zbl 0394.14008Mazur, B. 380 1977 Formal groups arising from algebraic varieties. Zbl 0351.14023Artin, M.; Mazur, B. 52 1977 Rational points on modular curves. Zbl 0357.14005Mazur, B. 25 1977 Points rationnels des courbes modulaires \(X_0(N)\). Zbl 0346.14013Mazur, Barry; Serre, Jean-Pierre 3 1976 Eigenvalues of Frobenius acting on algebraic varieties over finite fields. Zbl 0306.14011Mazur, B. 4 1975 ...and 29 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,187 Authors 42 Mazur, Barry 24 Lei, Antonio 23 Hida, Haruzo 22 Rubin, Karl Cooper 19 Lim, Meng Fai 18 Shlapentokh, Alexandra 17 Najman, Filip 15 Darmon, Henri René 15 Kamienny, Sheldon 14 Bleher, Frauke M. 13 Bertolini, Massimo 13 Büyükboduk, Kâzim 13 Friedlander, Eric Mark 13 González-Jiménez, Enrique 12 Dummigan, Neil 12 Ichimura, Humio 11 Bandini, Andrea 11 Dujella, Andrej 11 Khare, Chandrashekhar 11 Lozano-Robledo, Álvaro 11 Perrin-Riou, Bernadette 11 Porter, Timothy 10 Balakrishnan, Jennifer S. 10 Böckle, Gebhard 10 Calegari, Frank 10 Chen, Imin 10 Kurihara, Masato 10 Longhi, Ignazio 10 Pasten, Hector V. 10 Ribet, Kenneth Alan 10 Siksek, Samir 9 Byeon, Dongho 9 Castella, Francesc 9 Chinburg, Ted 9 Emerton, Matthew 9 Gross, Benedict Hyman 9 Ochiai, Tadashi 9 Panchishkin, Alexei A. 9 Poonen, Bjorn 9 Ray, Anwesh 9 Tilouine, Jacques 9 Vâjâitu, Marian 9 Wiles, Andrew John 8 Bellaïche, Joël 8 Buium, Alexandru 8 Clark, Peter Louis 8 Coleman, Robert Frederick 8 Conrad, Brian 8 Delbourgo, Daniel 8 Gee, Toby 8 Greenberg, Ralph 8 Greither, Cornelius 8 Harris, Michael Howard 8 Jeon, Daeyeol 8 Klosin, Krzysztof 8 Longo, Matteo 8 Murty, Maruti Ram 8 Silverberg, Alice 8 Stein, William A. 8 Stoll, Michael 8 Ramdorai, Sujatha 8 Tornero, José María 8 Trihan, Fabien 8 Vigni, Stefano 8 Yoo, Hwajong 8 Zaharescu, Alexandru 8 Zarkhin, Yuriĭ Gennad’evich 7 Achter, Jeffrey D. 7 Agashe, Amod 7 Bennett, Michael A. 7 Cegarra, Antonio Martínez 7 Cornelissen, Gunther 7 Daniels, Harris B. 7 Dieulefait, Luis Victor 7 Fisher, Tom A. 7 Kato, Kazuya 7 Kundu, Debanjana 7 Momose, Fumiyuki 7 Pál, Ambrus 7 Papikian, Mihran 7 Tamagawa, Akio 7 Tan, Ki-Seng 7 Taylor, Richard Lawrence 7 Vatsal, Vinayak 7 Wan, Daqing 7 Wuthrich, Christian 6 Alexandru, Victor 6 Anni, Samuele 6 Arai, Keisuke 6 Barrera Salazar, Daniel 6 Boston, Nigel 6 Burungale, Ashay A. 6 Byszewski, Jakub 6 Česnavičius, Kęstutis 6 Coates, John H. 6 Dąbrowski, Andrzej Bogdan 6 de Shalit, Ehud 6 Derickx, Maarten 6 Dimitrov, Mladen 6 Edwards, David A. ...and 2,087 more Authors all top 5 Cited in 263 Serials 274 Journal of Number Theory 153 Inventiones Mathematicae 120 Transactions of the American Mathematical Society 112 Compositio Mathematica 95 Duke Mathematical Journal 90 Mathematische Annalen 74 Journal de Théorie des Nombres de Bordeaux 68 Journal of Algebra 68 International Journal of Number Theory 66 Annales de l’Institut Fourier 61 Journal of Pure and Applied Algebra 55 Advances in Mathematics 55 Proceedings of the American Mathematical Society 53 Mathematische Zeitschrift 47 Bulletin of the American Mathematical Society. New Series 44 Journal für die Reine und Angewandte Mathematik 43 Mathematics of Computation 39 Israel Journal of Mathematics 37 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 35 Manuscripta Mathematica 35 Bulletin of the American Mathematical Society 32 Journal of the American Mathematical Society 31 Topology and its Applications 29 Experimental Mathematics 24 Research in Number Theory 22 Mathematical Proceedings of the Cambridge Philosophical Society 22 Annals of Mathematics. Second Series 20 LMS Journal of Computation and Mathematics 19 Acta Arithmetica 19 Algebraic & Geometric Topology 18 Proceedings of the Japan Academy. Series A 18 Forum of Mathematics, Sigma 17 Publications Mathématiques 17 Documenta Mathematica 16 Journal of the European Mathematical Society (JEMS) 16 Comptes Rendus. Mathématique. Académie des Sciences, Paris 15 Rocky Mountain Journal of Mathematics 15 The Ramanujan Journal 15 Journal of the Institute of Mathematics of Jussieu 15 Algebra & Number Theory 14 Communications in Algebra 14 Bulletin de la Société Mathématique de France 13 Archiv der Mathematik 13 Annales Mathématiques du Québec 12 Cahiers de Topologie et Géométrie Différentielle Catégoriques 12 Nagoya Mathematical Journal 12 Journal of Algebraic Geometry 12 Research in the Mathematical Sciences 11 Journal of Soviet Mathematics 11 Publications of the Research Institute for Mathematical Sciences, Kyoto University 11 Tokyo Journal of Mathematics 11 Ergodic Theory and Dynamical Systems 9 Bulletin of the Australian Mathematical Society 9 Functiones et Approximatio. Commentarii Mathematici 9 Journal of the Ramanujan Mathematical Society 9 Selecta Mathematica. New Series 9 Geometry & Topology 8 Glasgow Mathematical Journal 8 Rendiconti del Seminario Matematico della Università di Padova 7 Journal of the Mathematical Society of Japan 7 Memoirs of the American Mathematical Society 7 Osaka Journal of Mathematics 7 Pacific Journal of Mathematics 7 Proceedings of the London Mathematical Society. Third Series 7 Forum Mathematicum 7 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 7 Finite Fields and their Applications 7 Journal of Homotopy and Related Structures 7 Kyoto Journal of Mathematics 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 European Journal of Mathematics 6 Mathematical Notes 6 Monatshefte für Mathematik 6 Tôhoku Mathematical Journal. Second Series 6 Journal of Symbolic Computation 6 International Journal of Mathematics 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 6 Journal of Mathematical Sciences (New York) 6 Acta Mathematica Sinica. English Series 6 Proceedings of the Japan Academy 5 Communications in Mathematical Physics 5 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Functional Analysis and its Applications 5 Geometriae Dedicata 5 Journal of the London Mathematical Society. Second Series 5 Mathematika 5 Linear Algebra and its Applications 5 Mémoires de la Société Mathématique de France. Nouvelle Série 5 Indagationes Mathematicae. New Series 5 Algebras and Representation Theory 5 Journal of the Australian Mathematical Society 5 Science China. Mathematics 4 Journal d’Analyse Mathématique 4 The Mathematical Intelligencer 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Bulletin of the London Mathematical Society 4 Canadian Mathematical Bulletin 4 Michigan Mathematical Journal 4 Proceedings of the Edinburgh Mathematical Society. Series II ...and 163 more Serials all top 5 Cited in 54 Fields 1,884 Number theory (11-XX) 1,142 Algebraic geometry (14-XX) 178 Algebraic topology (55-XX) 151 Manifolds and cell complexes (57-XX) 122 Category theory; homological algebra (18-XX) 114 Dynamical systems and ergodic theory (37-XX) 104 Group theory and generalizations (20-XX) 81 Commutative algebra (13-XX) 70 \(K\)-theory (19-XX) 54 Several complex variables and analytic spaces (32-XX) 49 Topological groups, Lie groups (22-XX) 47 Associative rings and algebras (16-XX) 45 Field theory and polynomials (12-XX) 42 Mathematical logic and foundations (03-XX) 40 Global analysis, analysis on manifolds (58-XX) 37 Differential geometry (53-XX) 29 General topology (54-XX) 22 Functions of a complex variable (30-XX) 20 Combinatorics (05-XX) 19 History and biography (01-XX) 15 Convex and discrete geometry (52-XX) 14 Nonassociative rings and algebras (17-XX) 14 Quantum theory (81-XX) 12 General and overarching topics; collections (00-XX) 11 Geometry (51-XX) 11 Computer science (68-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Information and communication theory, circuits (94-XX) 9 Measure and integration (28-XX) 9 Functional analysis (46-XX) 8 Partial differential equations (35-XX) 6 Probability theory and stochastic processes (60-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 5 Operator theory (47-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Real functions (26-XX) 4 Ordinary differential equations (34-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistics (62-XX) 3 Numerical analysis (65-XX) 3 Biology and other natural sciences (92-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Approximations and expansions (41-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 Systems theory; control (93-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. Updates and corrections should be made in Wikidata.