## Mazur, Barry

Compute Distance To:
 Author ID: mazur.barry Published as: Mazur, Barry; Mazur, B.; Mazur, B. C. Further Spellings: Mazur, Barry Charles External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 143 Publications since 1959, including 9 Books 23 Contributions as Editor · 7 Further Contributions Biographic References: 2 Publications Co-Authors: 103 Co-Authors with 104 Joint Publications 2,567 Co-Co-Authors
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### 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 J. 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 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
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### 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
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### 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)

### Citations contained in zbMATH Open

129 Publications have been cited 3,885 times in 2,769 Documents Cited by Year
Modular curves and the Eisenstein ideal. Zbl 0394.14008
Mazur, B.
1977
Rational isogenies of prime degree. (With an appendix by D. Goldfeld). Zbl 0386.14009
Mazur, B.
1978
Arithmetic moduli of elliptic curves. Zbl 0576.14026
Katz, Nicholas M.; Mazur, Barry
1985
Class fields of abelian extensions of $$\mathbb Q$$. Zbl 0545.12005
Mazur, B.; Wiles, A.
1984
Rational points of Abelian varieties with values in towers of number fields. Zbl 0245.14015
Mazur, Barry
1972
Etale homotopy. Zbl 0182.26001
Artin, M.; Mazur, B.
1969
On $$p$$-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028
Mazur, B.; Tate, J.; Teitelbaum, J.
1986
Arithmetic of Weil curves. Zbl 0281.14016
Mazur, B.; Swinnerton-Dyer, P.
1974
On periodic points. Zbl 0127.13401
Artin, M.; Mazur, B.
1965
Universal extensions and one dimensional crystalline cohomology. Zbl 0301.14016
Mazur, Barry; Messing, William
1974
An introduction to the deformation theory of Galois representations. Zbl 0901.11015
Mazur, Barry
1997
Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur. Zbl 0433.14032
Gross, Benedict H.
1980
Deforming Galois representations. Zbl 0714.11076
Mazur, B.
1989
The eigencurve. Zbl 0932.11030
Coleman, R.; Mazur, B.
1998
On $$p$$-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008
Mazur, B.; Wiles, A.
1986
Geometric Galois representations. Zbl 0839.14011
Fontaine, Jean-Marc; Mazur, Barry
1995
A note on some contractible 4-manifolds. Zbl 0127.13604
Mazur, B.
1961
Formal groups arising from algebraic varieties. Zbl 0351.14023
Artin, M.; Mazur, B.
1977
Frobenius and the Hodge filtration. Zbl 0258.14006
Mazur, B.
1972
The square-free sieve and the rank of elliptic curves. Zbl 0725.11027
Gouvêa, F.; Mazur, B.
1991
Kolyvagin systems. Zbl 1055.11041
Mazur, Barry; Rubin, Karl
2004
Smoothings of piecewise linear manifolds. Zbl 0298.57007
Hirsch, Morris W.; Mazur, Barry
1974
Uniformity of rational points. Zbl 0872.14017
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1997
Frobenius and the Hodge filtration (estimates). Zbl 0261.14005
Mazur, B.
1973
Ranks of twists of elliptic curves and Hilbert’s tenth problem. Zbl 1227.11075
Mazur, B.; Rubin, K.
2010
Galois representations, Kähler differentials and “main conjectures”. (Représentations galoisiennes, différentielles de Kähler et “conjectures principales”.) Zbl 0744.11053
Mazur, B.; Tilouine, J.
1990
The topology of rational points. Zbl 0784.14012
Mazur, Barry
1992
Filtrations on the homology of algebraic varieties. Zbl 0841.14019
Friedlander, Eric M.; Mazur, Barry
1994
On the arithmetic of special values of L functions. Zbl 0426.14009
Mazur, B.
1979
Arithmetic on curves. Zbl 0593.14021
Mazur, Barry
1986
On embeddings of spheres. Zbl 0086.37004
Mazur, Barry
1959
Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004
Mazur, B.; Tate, J.
1987
Canonical height pairings via biextensions. Zbl 0574.14036
Mazur, B.; Tate, J.
1983
Finding large Selmer rank via an arithmetic theory of local constants. Zbl 1219.11084
Mazur, Barry; Rubin, Karl
2007
Local Euler characteristics. Zbl 0191.19202
Mazur, B.; Roberts, L.
1970
Notes on etale cohomology of number fields. Zbl 0282.14004
Mazur, Barry
1973
Questions of decidability and undecidability in number theory. Zbl 0814.11059
Mazur, B.
1994
Families of modular eigenforms. Zbl 0773.11030
Gouvêa, F.; Mazur, B.
1992
Visualizing elements in the Shafarevich-Tate group. Zbl 0972.11049
Cremona, John E.; Mazur, Barry
2000
On the van Kampen theorem. Zbl 0138.18301
Artin, M.; Mazur, B.
1966
Rational points on modular curves. Zbl 0357.14005
Mazur, B.
1977
Points of order 13 on elliptic curves. Zbl 0268.14009
Mazur, B.; Tate, J.
1973
Modular curves and arithmetic. Zbl 0597.14023
Mazur, B.
1984
Courbes elliptiques et symboles modulaires. Zbl 0276.14012
Mazur, Barry
1973
Rational torsion of prime order in elliptic curves over number fields (with an appendix by A. Granville). Zbl 0846.14012
Kamienny, S.; Mazur, B.
1995
Disparity in Selmer ranks of quadratic twists of elliptic curves. Zbl 1300.11063
Klagsbrun, Zev; Mazur, Barry; Rubin, Karl
2013
Hypersurfaces of low degree. Zbl 0991.14018
Harris, Joe; Mazur, Barry; Pandharipande, Rahul
1998
Nearly ordinary Galois deformations over arbitrary number fields. Zbl 1211.11065
Calegari, Frank; Mazur, Barry
2009
The $$p$$-adic sigma function. Zbl 0735.14020
Mazur, B.; Tate, J.
1991
Finding meaning in error terms. Zbl 1229.11001
Mazur, Barry
2008
Twisting commutative algebraic groups. Zbl 1128.14034
Mazur, B.; Rubin, K.; Silverberg, A.
2007
Evolutions, symbolic squares, and Fitting ideals. Zbl 0912.13010
Eisenbud, David; Mazur, Barry
1997
Relative neighborhoods and the theorems of Smale. Zbl 0112.38301
Mazur, B.
1963
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 1084.11033
Agashe, Amod; Stein, William
2005
Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032
Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark
2007
Computation of $$p$$-adic heights and log convergence. Zbl 1135.11034
Mazur, Barry; Stein, William; Tate, John
2007
Two-dimensional representations in the arithmetic of modular curves. Zbl 0780.14015
Mazur, B.; Ribet, K. A.
1991
Differential topology from the point of view of simple homotopy theory. Zbl 0173.51203
Mazur, Barry
1963
Relative modular symbols and Rankin-Selberg convolutions. Zbl 0941.11020
Kazhdan, D.; Mazur, B.; Schmidt, C.-G.
2000
Local flat duality. Zbl 0199.24501
Mazur, B.
1970
On the passage from local to global in number theory. Zbl 0813.14016
Mazur, B.
1993
Number theory as gadfly. Zbl 0764.11021
Mazur, B.
1991
The method of infinite repetition in pure topology. I. Zbl 0133.16506
Mazur, B.
1964
On monodromy invariants occurring in global arithmetic, and Fontaine’s theory. Zbl 0846.11039
Mazur, B.
1994
Explicit universal deformations of Galois representations. Zbl 0739.11021
Boston, N.; Mazur, B.
1989
Mathematics: frontiers and perspectives. Zbl 1047.00015
2000
The theme of $$p$$-adic variation. Zbl 0959.14008
Mazur, Barry
2000
The spin of prime ideals. Zbl 1296.11150
Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K.
2013
Open problems regarding rational points on curves and varieties. Zbl 0943.14009
Mazur, B.
1998
Speculations about the topology of rational points: An up-date. Zbl 0851.14009
Mazur, B.
1995
Analogies between function fields and number fields. Zbl 0531.12015
Mazur, B.; Wiles, A.
1983
How many rational points can a curve have? Zbl 0862.14012
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1995
Rational connectivity and sections of families over curves. Zbl 1092.14062
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2005
Controlling Selmer groups in the higher core rank case. Zbl 1411.11065
Mazur, Barry; Rubin, Karl
2016
Refined class number formulas and Kolyvagin systems. Zbl 1225.11144
Mazur, Barry; Rubin, Karl
2011
An “infinite fern” in the universal deformation space of Galois representations. Zbl 0865.11046
Mazur, B.
1997
Courbes de Weil de conducteur 26. Zbl 0241.14015
Mazur, Barry; Velu, Jacques
1972
Elliptic curves and class field theory. Zbl 1036.11023
Mazur, Barry; Rubin, Karl
2002
On the characteristic power series of the $$U$$ operator. Zbl 0779.11022
Gouvêa, F. Q.; Mazur, B.
1993
Two-dimensional $$p$$-adic Galois representations unramified away from $$p$$. Zbl 0773.11036
Mazur, B.
1990
A Markov model for Selmer ranks in families of twists. Zbl 1316.11045
Klagsbrun, Zev; Mazur, Barry; Rubin, Karl
2014
Perturbations, deformations, and variations (and “near-misses”) in geometry, physics, and number theory. Zbl 1057.11033
Mazur, B.
2004
On the density of modular representations. Zbl 1134.11324
Gouvêa, Fernando Q.; Mazur, Barry
1998
Growth of Selmer rank in nonabelian extensions of number fields. Zbl 1151.11023
Mazur, Barry; Rubin, Karl
2008
Rational families of $$17$$-torsion points of elliptic curves over number fields. Zbl 1440.11092
Derickx, Maarten; Mazur, Barry; Kamienny, Sheldon
2018
Visualizing elements of order three in the Shafarevich-Tate group. Zbl 0958.11043
Mazur, B.
1999
Abelian varieties and the Mordell-Lang conjecture. Zbl 0990.14006
Mazur, Barry
2000
How can we construct abelian Galois extensions of basic number fields? Zbl 1228.11163
Mazur, Barry
2011
Refined class number formulas for $$\mathbb{G}_m$$. Zbl 1414.11155
Mazur, Barry; Rubin, Karl
2016
Questions about powers of numbers. Zbl 1041.11065
Mazur, Barry
2000
Correspondence homomorphisms for singular varieties. Zbl 0811.14007
Friedlander, Eric M.; Mazur, Barry
1994
Organizing the arithmetic of elliptic curves. Zbl 1122.11038
Mazur, Barry; Rubin, Karl
2005
Studying the growth of Mordell-Weil. Zbl 1142.11339
Mazur, Barry; Rubin, Karl
2003
Open problems: descending cohomology, geometrically. Zbl 1317.11004
Mazur, Barry
2014
Diophantine stability. Zbl 06924832
Mazur, Barry; Rubin, Karl; Larsen, Michael
2018
Eigenvalues of Frobenius acting on algebraic varieties over finite fields. Zbl 0306.14011
Mazur, B.
1975
On embeddings of spheres. Zbl 0096.37904
Mazur, B. C.
1961
Symmetric homology spheres. Zbl 0103.39503
Mazur, Barry
1962
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 0446.14001
Zariski, Oscar
1978
Homotopy of varieties in the etale topology. Zbl 0188.53402
Artin, M.; Mazur, B.
1967
Rational families of $$17$$-torsion points of elliptic curves over number fields. Zbl 1440.11092
Derickx, Maarten; Mazur, Barry; Kamienny, Sheldon
2018
Diophantine stability. Zbl 06924832
Mazur, Barry; Rubin, Karl; Larsen, Michael
2018
Controlling Selmer groups in the higher core rank case. Zbl 1411.11065
Mazur, Barry; Rubin, Karl
2016
Refined class number formulas for $$\mathbb{G}_m$$. Zbl 1414.11155
Mazur, Barry; Rubin, Karl
2016
Alexandre Grothendieck 1928–2014, part 2. Zbl 1338.01023
Ladegaillerie, Yves; Lichtenbaum, Stephen; Lochak, Pierre; Mazur, Barry; Messing, William; Murre, Jacob; Schneps, Leila
2016
Prime numbers and the Riemann hypothesis. Zbl 1356.11001
Mazur, Barry; Stein, William
2016
A celebration of the mathematical work of Glenn Stevens. Zbl 1354.11004
Mazur, Barry
2016
Selmer companion curves. Zbl 1316.11047
Mazur, Barry; Rubin, Karl
2015
Erratum to: “The spin of prime ideals”. Zbl 1330.11072
Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K.
2015
A Markov model for Selmer ranks in families of twists. Zbl 1316.11045
Klagsbrun, Zev; Mazur, Barry; Rubin, Karl
2014
Open problems: descending cohomology, geometrically. Zbl 1317.11004
Mazur, Barry
2014
Is it plausible? Zbl 1307.11003
Mazur, Barry
2014
Disparity in Selmer ranks of quadratic twists of elliptic curves. Zbl 1300.11063
Klagsbrun, Zev; Mazur, Barry; Rubin, Karl
2013
The spin of prime ideals. Zbl 1296.11150
Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K.
2013
Circles disturbed. The interplay of mathematics and narrative. Zbl 1237.00022
2012
Refined class number formulas and Kolyvagin systems. Zbl 1225.11144
Mazur, Barry; Rubin, Karl
2011
How can we construct abelian Galois extensions of basic number fields? Zbl 1228.11163
Mazur, Barry
2011
Ranks of twists of elliptic curves and Hilbert’s tenth problem. Zbl 1227.11075
Mazur, B.; Rubin, K.
2010
Nearly ordinary Galois deformations over arbitrary number fields. Zbl 1211.11065
Calegari, Frank; Mazur, Barry
2009
Finding meaning in error terms. Zbl 1229.11001
Mazur, Barry
2008
Growth of Selmer rank in nonabelian extensions of number fields. Zbl 1151.11023
Mazur, Barry; Rubin, Karl
2008
Current developments in mathematics, 2006. Zbl 1149.00018
2008
Mathematical Platonism and its opposites. Zbl 1154.00310
Mazur, Barry
2008
Finding large Selmer rank via an arithmetic theory of local constants. Zbl 1219.11084
Mazur, Barry; Rubin, Karl
2007
Twisting commutative algebraic groups. Zbl 1128.14034
Mazur, B.; Rubin, K.; Silverberg, A.
2007
Average ranks of elliptic curves: tension between data and conjecture. Zbl 1190.11032
Bektemirov, Baur; Mazur, Barry; Stein, William; Watkins, Mark
2007
Computation of $$p$$-adic heights and log convergence. Zbl 1135.11034
Mazur, Barry; Stein, William; Tate, John
2007
Fearless symmetry. Exposing the hidden patterns of numbers. With a foreword by Barry Mazur. Zbl 1111.11001
Ash, Avner; Gross, Robert
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 1084.11033
Agashe, Amod; Stein, William
2005
Rational connectivity and sections of families over curves. Zbl 1092.14062
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2005
Organizing the arithmetic of elliptic curves. Zbl 1122.11038
Mazur, Barry; Rubin, Karl
2005
Finding large Selmer groups. Zbl 1211.11068
Mazur, Barry; Rubin, Karl
2005
Kolyvagin systems. Zbl 1055.11041
Mazur, Barry; Rubin, Karl
2004
Perturbations, deformations, and variations (and “near-misses”) in geometry, physics, and number theory. Zbl 1057.11033
Mazur, B.
2004
Arithmetic questions related to rationally connected varieties. Zbl 1071.14053
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason
2004
Jumps in Mordell-Weil rank and arithmetic surjectivity. Zbl 1075.14021
Graber, Tom; Harris, Joseph; Mazur, Barry; Starr, Jason
2004
What is …a motive? Zbl 1054.14511
Mazur, Barry
2004
Pairings in the arithmetic of elliptic curves. Zbl 1071.11028
Mazur, Barry; Rubin, Karl
2004
Studying the growth of Mordell-Weil. Zbl 1142.11339
Mazur, Barry; Rubin, Karl
2003
Current developments in mathematics, 2003. Zbl 1090.00008
2003
Imagining numbers. Particularly the square root of minus fifteen. Zbl 1049.00502
Mazur, Barry
2003
Elliptic curves and class field theory. Zbl 1036.11023
Mazur, Barry; Rubin, Karl
2002
La Nave, Federica; Mazur, Barry
2002
Visualizing elements in the Shafarevich-Tate group. Zbl 0972.11049
Cremona, John E.; Mazur, Barry
2000
Relative modular symbols and Rankin-Selberg convolutions. Zbl 0941.11020
Kazhdan, D.; Mazur, B.; Schmidt, C.-G.
2000
Mathematics: frontiers and perspectives. Zbl 1047.00015
2000
The theme of $$p$$-adic variation. Zbl 0959.14008
Mazur, Barry
2000
Abelian varieties and the Mordell-Lang conjecture. Zbl 0990.14006
Mazur, Barry
2000
Questions about powers of numbers. Zbl 1041.11065
Mazur, Barry
2000
Visualizing elements of order three in the Shafarevich-Tate group. Zbl 0958.11043
Mazur, B.
1999
The eigencurve. Zbl 0932.11030
Coleman, R.; Mazur, B.
1998
Hypersurfaces of low degree. Zbl 0991.14018
Harris, Joe; Mazur, Barry; Pandharipande, Rahul
1998
Open problems regarding rational points on curves and varieties. Zbl 0943.14009
Mazur, B.
1998
On the density of modular representations. Zbl 1134.11324
Gouvêa, Fernando Q.; Mazur, Barry
1998
An introduction to the deformation theory of Galois representations. Zbl 0901.11015
Mazur, Barry
1997
Uniformity of rational points. Zbl 0872.14017
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1997
Evolutions, symbolic squares, and Fitting ideals. Zbl 0912.13010
Eisenbud, David; Mazur, Barry
1997
An “infinite fern” in the universal deformation space of Galois representations. Zbl 0865.11046
Mazur, B.
1997
Conjecture. Zbl 1052.00513
Mazur, B.
1997
Geometric Galois representations. Zbl 0839.14011
Fontaine, Jean-Marc; Mazur, Barry
1995
Rational torsion of prime order in elliptic curves over number fields (with an appendix by A. Granville). Zbl 0846.14012
Kamienny, S.; Mazur, B.
1995
Speculations about the topology of rational points: An up-date. Zbl 0851.14009
Mazur, B.
1995
How many rational points can a curve have? Zbl 0862.14012
Caporaso, Lucia; Harris, Joe; Mazur, Barry
1995
Searching for $$p$$-adic eigenfunctions. Zbl 0851.11031
Gouvêa, Fernando Q.; Mazur, Barry
1995
Fermat’s last theorem. A lecture presented in Vancouver, British Columbia, Canada, August 1993. Videotape (NTSC). Zbl 0974.11500
Mazur, Barry
1995
Filtrations on the homology of algebraic varieties. Zbl 0841.14019
Friedlander, Eric M.; Mazur, Barry
1994
Questions of decidability and undecidability in number theory. Zbl 0814.11059
Mazur, B.
1994
On monodromy invariants occurring in global arithmetic, and Fontaine’s theory. Zbl 0846.11039
Mazur, B.
1994
Correspondence homomorphisms for singular varieties. Zbl 0811.14007
Friedlander, Eric M.; Mazur, Barry
1994
On the passage from local to global in number theory. Zbl 0813.14016
Mazur, B.
1993
On the characteristic power series of the $$U$$ operator. Zbl 0779.11022
Gouvêa, F. Q.; Mazur, B.
1993
The topology of rational points. Zbl 0784.14012
Mazur, Barry
1992
Families of modular eigenforms. Zbl 0773.11030
Gouvêa, F.; Mazur, B.
1992
The square-free sieve and the rank of elliptic curves. Zbl 0725.11027
Gouvêa, F.; Mazur, B.
1991
The $$p$$-adic sigma function. Zbl 0735.14020
Mazur, B.; Tate, J.
1991
Two-dimensional representations in the arithmetic of modular curves. Zbl 0780.14015
Mazur, B.; Ribet, K. A.
1991
Number theory as gadfly. Zbl 0764.11021
Mazur, B.
1991
A note on a classical theorem of Blichfeldt. Zbl 0746.52021
Gillet, H.; Mazur, B.; Soulé, C.
1991
Galois representations, Kähler differentials and “main conjectures”. (Représentations galoisiennes, différentielles de Kähler et “conjectures principales”.) Zbl 0744.11053
Mazur, B.; Tilouine, J.
1990
Two-dimensional $$p$$-adic Galois representations unramified away from $$p$$. Zbl 0773.11036
Mazur, B.
1990
Deforming Galois representations. Zbl 0714.11076
Mazur, B.
1989
Explicit universal deformations of Galois representations. Zbl 0739.11021
Boston, N.; Mazur, B.
1989
Refined conjectures of the “Birch and Swinnerton-Dyer type”. Zbl 0636.14004
Mazur, B.; Tate, J.
1987
On $$p$$-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Zbl 0699.14028
Mazur, B.; Tate, J.; Teitelbaum, J.
1986
On $$p$$-adic analytic families of Galois representations. (Appendix by Nigel Boston). Zbl 0654.12008
Mazur, B.; Wiles, A.
1986
Arithmetic on curves. Zbl 0593.14021
Mazur, Barry
1986
Arithmetic moduli of elliptic curves. Zbl 0576.14026
Katz, Nicholas M.; Mazur, Barry
1985
Class fields of abelian extensions of $$\mathbb Q$$. Zbl 0545.12005
Mazur, B.; Wiles, A.
1984
Modular curves and arithmetic. Zbl 0597.14023
Mazur, B.
1984
Canonical height pairings via biextensions. Zbl 0574.14036
Mazur, B.; Tate, J.
1983
Analogies between function fields and number fields. Zbl 0531.12015
Mazur, B.; Wiles, A.
1983
Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur. Zbl 0433.14032
Gross, Benedict H.
1980
On the arithmetic of special values of L functions. Zbl 0426.14009
Mazur, B.
1979
Rational isogenies of prime degree. (With an appendix by D. Goldfeld). Zbl 0386.14009
Mazur, B.
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 0446.14001
Zariski, Oscar
1978
Modular curves and the Eisenstein ideal. Zbl 0394.14008
Mazur, B.
1977
Formal groups arising from algebraic varieties. Zbl 0351.14023
Artin, M.; Mazur, B.
1977
Rational points on modular curves. Zbl 0357.14005
Mazur, B.
1977
Points rationnels des courbes modulaires $$X_0(N)$$. Zbl 0346.14013
Mazur, Barry; Serre, Jean-Pierre
1976
Eigenvalues of Frobenius acting on algebraic varieties over finite fields. Zbl 0306.14011
Mazur, B.
1975
...and 29 more Documents
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### Cited by 2,162 Authors

 42 Mazur, Barry 23 Hida, Haruzo 22 Lei, Antonio 22 Rubin, Karl Cooper 18 Shlapentokh, Alexandra 17 Lim, Meng Fai 17 Najman, Filip 15 Darmon, Henri René 15 Kamienny, Sheldon 14 Bleher, Frauke M. 13 Bertolini, Massimo 13 Friedlander, Eric Mark 12 Büyükboduk, Kâzim 12 Dummigan, Neil 12 González-Jiménez, Enrique 11 Dujella, Andrej 11 Ichimura, Humio 11 Khare, Chandrashekhar 11 Lozano-Robledo, Álvaro 11 Perrin-Riou, Bernadette 11 Porter, Timothy 10 Balakrishnan, Jennifer S. 10 Bandini, Andrea 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 Castella, Francesc 9 Chinburg, Ted 9 Emerton, Matthew 9 Gross, Benedict Hyman 9 Ochiai, Tadashi 9 Panchishkin, Alexei A. 9 Poonen, Bjorn 9 Tilouine, Jacques 9 Vâjâitu, Marian 9 Wiles, Andrew John 8 Bellaïche, Joël 8 Buium, Alexandru 8 Byeon, Dongho 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 Ray, Anwesh 8 Silverberg, Alice 8 Stein, William A. 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 Dieulefait, Luis Victor 7 Fisher, Tom A. 7 Kato, Kazuya 7 Momose, Fumiyuki 7 Pál, Ambrus 7 Papikian, Mihran 7 Stoll, Michael 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 Daniels, Harris B. 6 de Shalit, Ehud 6 Derickx, Maarten 6 Edwards, David A. 6 Frey, Gerhard 6 Geoghegan, Ross ...and 2,062 more Authors
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### Cited in 260 Serials

 273 Journal of Number Theory 152 Inventiones Mathematicae 120 Transactions of the American Mathematical Society 112 Compositio Mathematica 95 Duke Mathematical Journal 89 Mathematische Annalen 72 Journal de Théorie des Nombres de Bordeaux 68 Journal of Algebra 66 International Journal of Number Theory 64 Annales de l’Institut Fourier 61 Journal of Pure and Applied Algebra 54 Proceedings of the American Mathematical Society 53 Advances in Mathematics 52 Mathematische Zeitschrift 47 Bulletin of the American Mathematical Society. New Series 43 Mathematics of Computation 42 Journal für die Reine und Angewandte Mathematik 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 27 Experimental Mathematics 24 Research in Number Theory 22 Annals of Mathematics. Second Series 21 Mathematical Proceedings of the Cambridge Philosophical Society 20 LMS Journal of Computation and Mathematics 19 Algebraic & Geometric Topology 18 Proceedings of the Japan Academy. Series A 18 Forum of Mathematics, Sigma 17 Publications Mathématiques 17 Documenta Mathematica 16 Acta Arithmetica 15 Rocky Mountain Journal of Mathematics 15 Journal of the European Mathematical Society (JEMS) 15 Comptes Rendus. Mathématique. Académie des Sciences, Paris 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 14 The Ramanujan Journal 13 Annales Mathématiques du Québec 12 Archiv der Mathematik 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 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 7 Finite Fields and their Applications 7 Journal of Homotopy and Related Structures 6 Mathematical Notes 6 Monatshefte für Mathematik 6 Tohoku 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 6 Kyoto Journal of Mathematics 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 European Journal of Mathematics 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 Forum Mathematicum 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 $$K$$-Theory ...and 160 more Serials
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### Cited in 54 Fields

 1,853 Number theory (11-XX) 1,127 Algebraic geometry (14-XX) 178 Algebraic topology (55-XX) 149 Manifolds and cell complexes (57-XX) 122 Category theory; homological algebra (18-XX) 114 Dynamical systems and ergodic theory (37-XX) 102 Group theory and generalizations (20-XX) 80 Commutative algebra (13-XX) 70 $$K$$-theory (19-XX) 51 Several complex variables and analytic spaces (32-XX) 48 Topological groups, Lie groups (22-XX) 47 Associative rings and algebras (16-XX) 43 Field theory and polynomials (12-XX) 42 Mathematical logic and foundations (03-XX) 40 Global analysis, analysis on manifolds (58-XX) 35 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) 13 Quantum theory (81-XX) 12 General and overarching topics; collections (00-XX) 11 Geometry (51-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Computer science (68-XX) 10 Information and communication theory, circuits (94-XX) 9 Measure and integration (28-XX) 9 Partial differential equations (35-XX) 9 Functional analysis (46-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 Numerical analysis (65-XX) 3 Relativity and gravitational theory (83-XX) 3 Biology and other natural sciences (92-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 2 Statistics (62-XX) 2 Mechanics of particles and systems (70-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)

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