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Katz, Nicholas Michael

Author ID: katz.nicholas-m Recent zbMATH articles by "Katz, Nicholas Michael"
Published as: Katz, Nicholas M.; Katz, N. M.; Katz, Nicholas; Katz, N.
Further Spellings: Katz, Nick; Кац, Николас М
Homepage: https://web.math.princeton.edu/~nmk/
External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
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Serials

10 IMRN. International Mathematics Research Notices
10 Finite Fields and their Applications
7 Annals of Mathematics Studies
6 Inventiones Mathematicae
4 American Journal of Mathematics
4 Publications Mathématiques
4 Mathematische Annalen
4 L’Enseignement Mathématique. 2e Série
4 Experimental Mathematics
3 Journal für die Reine und Angewandte Mathematik
3 Forum Mathematicum
3 Bulletin of the American Mathematical Society. New Series
3 Notices of the American Mathematical Society
3 Progress in Mathematics
3 Modern Birkhäuser Classics
2 Advances in Mathematics
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Bulletin de la Société Mathématique de France
2 Duke Mathematical Journal
2 Mathematika
2 Journal of the American Mathematical Society
2 Geometric and Functional Analysis. GAFA
2 Annals of Mathematics. Second Series
1 Israel Journal of Mathematics
1 Acta Arithmetica
1 Annales de l’Institut Fourier
1 Compositio Mathematica
1 Journal of Algebra
1 Journal of the Faculty of Science. Section I A
1 Journal of Mathematics of Kyoto University
1 Journal of Number Theory
1 Journal of Pure and Applied Algebra
1 Mathematische Zeitschrift
1 Proceedings of the London Mathematical Society. Third Series
1 Transactions of the American Mathematical Society
1 Comptes Rendus de l’Académie des Sciences. Série I
1 Mathematical Research Letters
1 Vietnam Journal of Mathematics
1 Journal of the European Mathematical Society (JEMS)
1 Moscow Mathematical Journal
1 Oberwolfach Reports
1 International Journal of Number Theory
1 Astérisque
1 Colloquium Publications. American Mathematical Society
1 Lecture Notes in Mathematics
1 Communications in Number Theory and Physics
1 Cambridge Journal of Mathematics
1 Philosophical Transactions A. Royal Society of London
1 Tunisian Journal of Mathematics

Publications by Year

Citations contained in zbMATH Open

141 Publications have been cited 3,910 times in 2,701 Documents Cited by Year
Arithmetic moduli of elliptic curves. Zbl 0576.14026
Katz, Nicholas M.; Mazur, Barry
306
1985
Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004
Katz, Nicholas M.; Sarnak, Peter
280
1999
Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin. Zbl 0221.14007
Katz, Nicholas M.
232
1970
\(p\)-adic properties of modular schemes and modular forms. Zbl 0271.10033
Katz, Nicholas M.
212
1973
Gauss sums, Kloosterman sums, and monodromy groups. Zbl 0675.14004
Katz, Nicholas M.
197
1988
Exponential sums and differential equations. Zbl 0731.14008
Katz, Nicholas M.
180
1990
Zeroes of zeta functions and symmetry. Zbl 0921.11047
Katz, Nicholas M.; Sarnak, Peter
175
1999
Rigid local systems. Zbl 0864.14013
Katz, Nicholas M.
135
1996
\(p\)-adic \(L\)-functions for CM fields. Zbl 0417.12003
Katz, Nicholas M.
127
1978
\(p\)-adic interpolation of real analytic Eisenstein series. Zbl 0354.14007
Katz, Nicholas M.
122
1976
Some consequences of the Riemann hypothesis for varieties over finite fields. Zbl 0275.14011
Katz, Nicholas M.; Messing, William
121
1974
Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz. Zbl 1213.14020
Hausel, Tamás; Rodriguez-Villegas, Fernando
112
2008
Algebraic solutions of differential equations (p-curvature and the Hodge filtration). Zbl 0278.14004
Katz, Nicholas M.
94
1972
Slope filtration of F-crystals. Zbl 0426.14007
Katz, Nicholas M.
94
1979
On the differentiation of De Rham cohomology classes with respect to parameters. Zbl 0165.54802
Katz, N. M.; Oda, T.
81
1968
Galois properties of torsion points on abelian varieties. Zbl 0471.14023
Katz, Nicholas M.
72
1981
Serre-Tate local moduli. Zbl 0477.14007
Katz, N.
71
1981
On a theorem of Ax. Zbl 0237.12012
Katz, Nicholas M.
66
1971
On the calculation of some differential Galois groups. Zbl 0609.12025
Katz, Nicholas M.
62
1987
Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.). Zbl 0603.14015
Katz, Nicholas M.; Laumon, Gérard
61
1985
Local-to-global extensions of representations of fundamental groups. Zbl 0564.14013
Katz, Nicholas M.
56
1986
Séminaire de géométrie algébrique du Bois-Marie 1967–1969. Groupes de monodromie en géométrie algébrique (SGA 7 II) par P. Deligne et N. Katz. Exposés X à XXII. Zbl 0258.00005
52
1973
Finiteness theorems in geometric classfield theory. (With an appendix by Kenneth A. Ribet). Zbl 0495.14011
Katz, Nicholas M.; Lang, Serge
48
1981
Sommes exponentielles. Cours à Orsay, automne 1979. Redige par Gerard Laumon, preface par Luc Illusie. Zbl 0469.12007
Katz, Nicholas M.
39
1980
Higher congruences between modular forms. Zbl 0356.10020
Katz, Nicholas M.
36
1975
Travaux de Dwork. Zbl 0259.14007
Katz, Nicholas
34
1973
Sums of Betti numbers in arbitrary characteristic. Zbl 1068.14501
Katz, Nicholas M.
32
2001
A conjecture in the arithmetic theory of differential equations. Zbl 0504.12022
Katz, Nicholas M.
32
1982
Moments, monodromy, and perversity. A Diophantine perspective. Zbl 1079.14025
Katz, Nicholas M.
31
2005
The Eisenstein measure and p-adic interpolation. Zbl 0375.12022
Katz, Nicholas M.
30
1977
An estimate for character sums. Zbl 0672.10026
Katz, Nicholas M.
29
1989
On the monodromy groups attached to certain families of exponential sums. Zbl 0643.12004
Katz, Nicholas M.
28
1987
Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050
Poonen, Bjorn; Voloch, José Felipe
27
2004
Estimates for Soto-Andrade sums. Zbl 0798.11053
Katz, Nicholas M.
25
1993
A result on modular forms in characteristic p. Zbl 0392.10026
Katz, Nicholas M.
25
1977
On the differential equations satisfied by period matrices. Zbl 0159.22502
Katz, N. M.
25
1968
p-adic L-functions via moduli of elliptic curves. Zbl 0317.14009
Katz, Nicholas M.
24
1975
Estimates for “singular” exponential sums. Zbl 0991.11064
Katz, Nicholas M.
24
1999
Sommes de Kloosterman et courbes elliptiques universelles en caractéristiques 2 et 3. (Kloosterman sums and universal elliptic curves in characteristics 2 and 3). Zbl 0701.14033
Katz, Nicholas; Livné, Ron
24
1989
Crystalline cohomology, Dieudonne modules, and Jacobi sums. Zbl 0502.14007
Katz, Nicholas M.
23
1981
Convolution and equidistribution. Sato-Tate theorems for finite-field Mellin transforms. Zbl 1261.11084
Katz, Nicholas M.
22
2012
Pinceaux de Lefschetz: Théoreme d’existence. Zbl 0284.14006
Katz, N. M.
21
1973
Estimates for nonsingular multiplicative character sums. Zbl 1028.11075
Katz, Nicholas M.
21
2002
A general stratification theorem for exponential sums, and applications. Zbl 0986.11054
Fouvry, E.; Katz, N.
20
2001
Twisted \(L\)-functions and monodromy. Zbl 1029.14005
Katz, Nicholas M.
18
2002
The regularity theorem in algebraic geometry. Zbl 0235.14006
Katz, Nicholas M.
18
1971
An overview of Deligne’s work on Hilbert’s twenty-first problem. Zbl 0347.14010
Katz, Nicholas M.
17
1976
A simple algorithm for cyclic vectors. Zbl 0621.13003
Katz, Nicholas M.
17
1987
The divisor function over arithmetic progressions. With Appendix by Nicholas Katz. Zbl 0764.11040
Fouvry, Etienne; Iwaniec, Henryk
16
1992
Space filling curves over finite fields. Zbl 1016.11022
Katz, Nicholas M.
16
2001
Divisibilities, congruences, and Cartier duality. Zbl 0559.14032
Katz, Nicholas M.
15
1981
Another look at the Dwork family. Zbl 1195.14015
Katz, Nicholas M.
15
2009
Witt vectors and a question of Keating and Rudnick. Zbl 1328.13028
Katz, Nicholas M.
14
2013
Another look at \(p\)-adic \(L\)-functions for totally real fields. Zbl 0497.14006
Katz, Nicholas M.
14
1981
Une formule de congruence pour la fonction \(\zeta\). Zbl 0275.14015
Katz, N.
13
1973
Rigid local systems on \(\mathbb{A}^{1}\) with finite monodromy. Zbl 1456.11232
Katz, Nicholas M.
13
2018
Travaux de Laumon. (Works of Laumon). Zbl 0698.14014
Katz, Nicholas M.
13
1988
Exponential sums over finite fields and differential equations over the complex numbers: Some interactions. Zbl 0727.11057
Katz, Nicholas M.
13
1990
Formal groups and p-adic interpolation. Zbl 0351.14024
Katz, Nicholas M.
12
1977
Review of \(\ell\)-adic cohomology. Zbl 0817.14006
Katz, Nicholas M.
12
1994
Perversity and exponential sums. Zbl 0755.14008
Katz, Nicholas M.
11
1989
On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor. Zbl 1358.11127
Katz, Nicholas M.
10
2013
\(L\)-functions and monodromy: four lectures on Weil II. Zbl 1016.14011
Katz, Nicholas M.
10
2001
Internal reconstruction of unit-root F-crystals via expansion- coefficients. Appendix: ”Some results on partial Hodge-Witt decompositions” by Luc Illusie. Zbl 0592.14021
Katz, Nicholas M.
10
1985
Étude cohomologique des pinceaux de Lefschetz. Zbl 0284.14007
Katz, N.
10
1973
The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers. Zbl 0303.10028
Katz, Nicholas M.
10
1975
Affine cohomological transforms, perversity, and monodromy. Appendix (d’après Deligne). Zbl 0815.14011
Katz, Nicholas M.
10
1993
Larsen’s alternative, moments, and the monodromy of Lefschetz pencils. Zbl 1081.14015
Katz, Nicholas M.
9
2004
Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess. Zbl 1023.11031
Katz, Nicholas M.
9
2001
Notes on \(G_{2}\), determinants, and equidistribution. Zbl 1065.11060
Katz, Nicholas M.
9
2004
Factoring polynomials in finite fields: An application of Lang-Weil to a problem in graph theory. Zbl 0708.05029
Katz, Nicholas M.
9
1990
An overview of Deligne’s proof of the Riemann hypothesis for varieties over finite fields. Zbl 0339.14013
Katz, Nicholas M.
8
1976
A note on lower bounds for Frobenius traces. Zbl 1220.11078
Bombieri, Enrico; Katz, Nicholas M.
8
2010
Lang-Trotter revisited. Zbl 1234.11072
Katz, Nicholas M.
8
2009
The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume I. Zbl 0717.00008
7
1990
Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families. Zbl 1067.14504
de Jong, A. Johan; Katz, Nicholas M.
7
2000
\(G_2\) and hypergeometric sheaves. Zbl 1167.14013
Katz, Nicholas M.
7
2007
Rigid local systems and finite symplectic groups. Zbl 1459.11225
Katz, Nicholas M.; Tiep, Pham Huu
7
2019
Sato-Tate in the higher dimensional case: elaboration of 9.5.4 in Serre’s \(N_X(p)\) book. Zbl 1320.14042
Katz, Nicholas M.
6
2013
On the intersection matrix of a hypersurface. Zbl 0187.42802
Katz, Nicholas M.
6
1969
A semicontinuity result for monodromy under degeneration. Zbl 1070.14024
Katz, Nicholas M.
6
2003
Introduction aux travaux récents de Dwork. Zbl 0218.14011
Katz, N. M.
6
1971
Wieferich past and future. Zbl 1416.11082
Katz, Nicholas M.
6
2015
Estimates for nonsingular mixed character sums. Zbl 1145.11084
Katz, Nicholas M.
6
2007
Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\). Zbl 1446.11210
Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu
6
2020
Local systems and finite unitary and symplectic groups. Zbl 1425.14009
Katz, Nicholas M.; Tiep, Pham Huu
6
2019
Elliptic convolution, \(G_2\), and elliptic surfaces. Zbl 1326.14017
Katz, Nicholas M.
5
2015
On the uniform distribution of Gauss sums and Jacobi sums. Zbl 0866.11073
Katz, Nicholas M.; Zheng, Zhiyong
5
1996
Le théorème de Griffiths. Zbl 0271.14002
Katz, N.
5
1973
A note on exponential sums. Zbl 0851.11073
Katz, Nicholas M.
5
1995
Corrections to: A conjecture in the arithmetic theory of differential equations. Zbl 0513.12018
Katz, Nicholas M.
5
1982
Witt vectors and a question of Rudnick and Waxman. Zbl 1405.13040
Katz, Nicholas M.
5
2017
From Clausen to Carlitz: low-dimensional spin groups and identities among character sums. Zbl 1234.11103
Katz, Nicholas M.
5
2009
Rigid local systems and alternating groups. Zbl 1454.11217
Guralnick, Robert; Katz, Nicholas; Tiep, Pham Huu
5
2019
A rigid local system with monodromy group \(2.J_{2}\). Zbl 1467.11115
Katz, Nicholas M.; Rojas-León, Antonio
5
2019
A rigid local system with monodromy group the big Conway group \(2.\mathsf{Co}_1\) and two others with monodromy group the Suzuki group \(6.\mathsf{Suz}\). Zbl 1457.11169
Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu
5
2020
Monodromy of families of curves: Applications of some results of Davenport-Lewis. Zbl 0475.14025
Katz, Nicholas M.
4
1981
Le niveau de la cohomologie des intersections complètes. Appendice par P. Deligne. Zbl 0288.14001
Katz, N.
4
1973
On a question of Lillian Pierce. Zbl 1139.11055
Katz, Nicholas M.
4
2006
Rigid local systems and a question of Wootters. Zbl 1368.11131
Katz, Nicholas M.
4
2012
Monodromy groups of Kloosterman and hypergeometric sheaves. Zbl 1485.11166
Katz, Nicholas M.; Tiep, Pham Huu
3
2021
Exponential sums and total Weil representations of finite symplectic and unitary groups. Zbl 1486.11149
Katz, Nicholas M.; Tiep, Pham Huu
3
2021
Hypergeometric sheaves and finite symplectic and unitary groups. Zbl 1486.11150
Katz, Nicholas M.; Tiep, Pham Huu
3
2021
Rigid local systems and finite general linear groups. Zbl 1485.11165
Katz, Nicholas M.; Tiep, Pham Huu
2
2021
Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\). Zbl 1446.11210
Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu
6
2020
A rigid local system with monodromy group the big Conway group \(2.\mathsf{Co}_1\) and two others with monodromy group the Suzuki group \(6.\mathsf{Suz}\). Zbl 1457.11169
Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu
5
2020
Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_2\). Zbl 1460.11144
Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu
4
2020
Moments of Weil representations of finite special unitary groups. Zbl 1485.20038
Katz, Nicholas M.; Tiep, Pham Huu
1
2020
Rigid local systems and finite symplectic groups. Zbl 1459.11225
Katz, Nicholas M.; Tiep, Pham Huu
7
2019
Local systems and finite unitary and symplectic groups. Zbl 1425.14009
Katz, Nicholas M.; Tiep, Pham Huu
6
2019
Rigid local systems and alternating groups. Zbl 1454.11217
Guralnick, Robert; Katz, Nicholas; Tiep, Pham Huu
5
2019
A rigid local system with monodromy group \(2.J_{2}\). Zbl 1467.11115
Katz, Nicholas M.; Rojas-León, Antonio
5
2019
A note on Galois representations with big image. Zbl 1476.11137
Katz, Nicholas M.
3
2019
Exponential sums, Ree groups and Suzuki groups: conjectures. Zbl 1473.11219
Katz, Nicholas M.
1
2019
Rigid local systems on \(\mathbb{A}^{1}\) with finite monodromy. Zbl 1456.11232
Katz, Nicholas M.
13
2018
Witt vectors and a question of Rudnick and Waxman. Zbl 1405.13040
Katz, Nicholas M.
5
2017
\(G_{2}\) and some exceptional Witt vector identities. Zbl 1409.11131
Katz, Nicholas M.
1
2017
A note on random matrix integrals, moment identities, and Catalan numbers. Zbl 1350.22009
Katz, Nicholas M.
2
2016
Alexandre Grothendieck 1928–2014. I. Zbl 1338.01022
Atiyah, Michael; Bass, Hyman; Cartier, Pierre; Deligne, Pierre; Demazure, Michel; Greenberg, Marvin Jay; Hartshorne, Robin; Illusie, Luc; Katz, Nicholas; Kleiman, Steven L.
1
2016
Wieferich past and future. Zbl 1416.11082
Katz, Nicholas M.
6
2015
Elliptic convolution, \(G_2\), and elliptic surfaces. Zbl 1326.14017
Katz, Nicholas M.
5
2015
On a question of Rudnick: do we have square root cancellation for error terms in moment calculations? Zbl 1386.11094
Katz, Nicholas M.
2
2015
Witt vectors and a question of Entin, Keating, and Rudnick. Zbl 1346.13045
Katz, Nicholas M.
2
2015
On two questions of Entin, Keating, and Rudnick on primitive Dirichlet characters. Zbl 1385.11072
Katz, Nicholas M.
1
2015
Witt vectors and a question of Keating and Rudnick. Zbl 1328.13028
Katz, Nicholas M.
14
2013
On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor. Zbl 1358.11127
Katz, Nicholas M.
10
2013
Sato-Tate in the higher dimensional case: elaboration of 9.5.4 in Serre’s \(N_X(p)\) book. Zbl 1320.14042
Katz, Nicholas M.
6
2013
Convolution and equidistribution. Sato-Tate theorems for finite-field Mellin transforms. Zbl 1261.11084
Katz, Nicholas M.
22
2012
Rigid local systems and a question of Wootters. Zbl 1368.11131
Katz, Nicholas M.
4
2012
Report on the irreducibility of \(L\)-functions. Zbl 1276.11147
Katz, Nicholas M.
4
2012
A note on lower bounds for Frobenius traces. Zbl 1220.11078
Bombieri, Enrico; Katz, Nicholas M.
8
2010
Automorphic realization of residual Galois representations. Zbl 1257.11051
Guralnick, Robert; Harris, Michael; Katz, Nicholas M.
2
2010
2, 3, 5, Legendre: \(\pm \) trace ratios in families of elliptic curves. Zbl 1295.14026
Katz, Nicholas M.
1
2010
Another look at the Dwork family. Zbl 1195.14015
Katz, Nicholas M.
15
2009
Lang-Trotter revisited. Zbl 1234.11072
Katz, Nicholas M.
8
2009
From Clausen to Carlitz: low-dimensional spin groups and identities among character sums. Zbl 1234.11103
Katz, Nicholas M.
5
2009
On a question of Browning and Heath-Brown. Zbl 1253.11080
Katz, Nicholas M.
3
2009
On character sums with distances on the upper half plane over a finite field. Zbl 1253.11109
Katz, Nicholas M.; Shparlinski, Igor E.; Xiong, Maosheng
1
2009
Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz. Zbl 1213.14020
Hausel, Tamás; Rodriguez-Villegas, Fernando
112
2008
Estimates for mixed character sums. Zbl 1226.11129
Katz, Nicholas M.
2
2008
\(G_2\) and hypergeometric sheaves. Zbl 1167.14013
Katz, Nicholas M.
7
2007
Estimates for nonsingular mixed character sums. Zbl 1145.11084
Katz, Nicholas M.
6
2007
The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume I. Reprint of the 1990 edition. Zbl 1105.14003
2
2007
On a question of Lillian Pierce. Zbl 1139.11055
Katz, Nicholas M.
4
2006
Moments, monodromy, and perversity. A Diophantine perspective. Zbl 1079.14025
Katz, Nicholas M.
31
2005
Cohomological divisibility and point count divisibility. Zbl 1076.14028
Esnault, Hélène; Katz, Nicholas M.
2
2005
Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050
Poonen, Bjorn; Voloch, José Felipe
27
2004
Larsen’s alternative, moments, and the monodromy of Lefschetz pencils. Zbl 1081.14015
Katz, Nicholas M.
9
2004
Notes on \(G_{2}\), determinants, and equidistribution. Zbl 1065.11060
Katz, Nicholas M.
9
2004
Geometric aspects of Dwork theory. Vol. I, II. Zbl 1047.14001
1
2004
Inequalities related to Lefschetz pencils and integrals of Chern classes. Zbl 1092.14016
Katz, Nicholas M.; Pandharipande, Rahul
1
2004
A semicontinuity result for monodromy under degeneration. Zbl 1070.14024
Katz, Nicholas M.
6
2003
Estimates for nonsingular multiplicative character sums. Zbl 1028.11075
Katz, Nicholas M.
21
2002
Twisted \(L\)-functions and monodromy. Zbl 1029.14005
Katz, Nicholas M.
18
2002
Sums of Betti numbers in arbitrary characteristic. Zbl 1068.14501
Katz, Nicholas M.
32
2001
A general stratification theorem for exponential sums, and applications. Zbl 0986.11054
Fouvry, E.; Katz, N.
20
2001
Space filling curves over finite fields. Zbl 1016.11022
Katz, Nicholas M.
16
2001
\(L\)-functions and monodromy: four lectures on Weil II. Zbl 1016.14011
Katz, Nicholas M.
10
2001
Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess. Zbl 1023.11031
Katz, Nicholas M.
9
2001
Sato-Tate equidistribution of Kurlberg-Rudnick sums. Zbl 1011.11058
Katz, Nicholas M.
1
2001
Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families. Zbl 1067.14504
de Jong, A. Johan; Katz, Nicholas M.
7
2000
Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004
Katz, Nicholas M.; Sarnak, Peter
280
1999
Zeroes of zeta functions and symmetry. Zbl 0921.11047
Katz, Nicholas M.; Sarnak, Peter
175
1999
Estimates for “singular” exponential sums. Zbl 0991.11064
Katz, Nicholas M.
24
1999
Bernard Dwork (1923–1998). Zbl 1177.01050
Katz, Nicholas M.; Tate, John
2
1999
Rigid local systems. Zbl 0864.14013
Katz, Nicholas M.
135
1996
On the uniform distribution of Gauss sums and Jacobi sums. Zbl 0866.11073
Katz, Nicholas M.; Zheng, Zhiyong
5
1996
A note on exponential sums. Zbl 0851.11073
Katz, Nicholas M.
5
1995
Review of \(\ell\)-adic cohomology. Zbl 0817.14006
Katz, Nicholas M.
12
1994
Perversity and exponential sums. II: Estimates for and inequalities among \(A\)-numbers. Zbl 0837.14017
Katz, Nicholas M.
2
1994
Independence of \(\ell\) and weak Lefschetz. Zbl 0813.14013
Katz, Nicholas M.
1
1994
Estimates for Soto-Andrade sums. Zbl 0798.11053
Katz, Nicholas M.
25
1993
Affine cohomological transforms, perversity, and monodromy. Appendix (d’après Deligne). Zbl 0815.14011
Katz, Nicholas M.
10
1993
The divisor function over arithmetic progressions. With Appendix by Nicholas Katz. Zbl 0764.11040
Fouvry, Etienne; Iwaniec, Henryk
16
1992
Exponential sums and differential equations. Zbl 0731.14008
Katz, Nicholas M.
180
1990
Exponential sums over finite fields and differential equations over the complex numbers: Some interactions. Zbl 0727.11057
Katz, Nicholas M.
13
1990
Factoring polynomials in finite fields: An application of Lang-Weil to a problem in graph theory. Zbl 0708.05029
Katz, Nicholas M.
9
1990
The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume I. Zbl 0717.00008
7
1990
The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume II. Zbl 0717.00009
2
1990
The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume III. Zbl 0717.00010
1
1990
An estimate for character sums. Zbl 0672.10026
Katz, Nicholas M.
29
1989
Sommes de Kloosterman et courbes elliptiques universelles en caractéristiques 2 et 3. (Kloosterman sums and universal elliptic curves in characteristics 2 and 3). Zbl 0701.14033
Katz, Nicholas; Livné, Ron
24
1989
Perversity and exponential sums. Zbl 0755.14008
Katz, Nicholas M.
11
1989
Corrections à: “Transformation de Fourier et majoration de sommes exponentielles”. (Corrections to: “Fourier transformation and majorization of exponential sums”). Zbl 0705.14020
Katz, Nicholas M.; Laumon, Gérard
2
1989
Gauss sums, Kloosterman sums, and monodromy groups. Zbl 0675.14004
Katz, Nicholas M.
197
1988
Travaux de Laumon. (Works of Laumon). Zbl 0698.14014
Katz, Nicholas M.
13
1988
On the calculation of some differential Galois groups. Zbl 0609.12025
Katz, Nicholas M.
62
1987
On the monodromy groups attached to certain families of exponential sums. Zbl 0643.12004
Katz, Nicholas M.
28
1987
A simple algorithm for cyclic vectors. Zbl 0621.13003
Katz, Nicholas M.
17
1987
A note on pseudo-CM representations and differential Galois groups. Zbl 0643.12007
Katz, Nicholas M.; Pink, Richard
4
1987
On a certain class of exponential sums. Zbl 0604.12015
Katz, Nicholas M.
2
1987
Local-to-global extensions of representations of fundamental groups. Zbl 0564.14013
Katz, Nicholas M.
56
1986
Arithmetic moduli of elliptic curves. Zbl 0576.14026
Katz, Nicholas M.; Mazur, Barry
306
1985
Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.). Zbl 0603.14015
Katz, Nicholas M.; Laumon, Gérard
61
1985
Internal reconstruction of unit-root F-crystals via expansion- coefficients. Appendix: ”Some results on partial Hodge-Witt decompositions” by Luc Illusie. Zbl 0592.14021
Katz, Nicholas M.
10
1985
Expansion-coefficients as approximate solution of differential equations. Zbl 0561.14010
Katz, Nicholas M.
2
1984
Wild ramification and some problems of ”independence of \(\ell ''\). Zbl 0568.14012
Katz, Nicholas M.
3
1983
On the ubiquity of ”pathology” in products. Zbl 0574.14021
Katz, Nicholas M.
2
1983
A conjecture in the arithmetic theory of differential equations. Zbl 0504.12022
Katz, Nicholas M.
32
1982
Corrections to: A conjecture in the arithmetic theory of differential equations. Zbl 0513.12018
Katz, Nicholas M.
5
1982
...and 41 more Documents
all top 5

Cited by 2,291 Authors

48 Katz, Nicholas Michael
32 Shparlinski, Igor E.
24 Kowalski, Emmanuel
24 Miller, Steven J.
22 Wan, Daqing
21 Hida, Haruzo
21 Michel, Philippe Gabriel
20 Sawin, William F.
19 Sperber, Steven I.
18 Tiep Pham Huu
16 Fouvry, Etienne
16 Keating, Jonathan Peter
15 Rojas-León, Antonio
14 Adolphson, Alan
14 Esnault, Hélène
14 Zaharescu, Alexandru
13 Gross, Benedict Hyman
13 Harris, Michael Howard
13 Panchishkin, Alexei A.
12 Burungale, Ashay A.
11 Buium, Alexandru
11 Xi, Ping
10 Barman, Rupam
10 Biswas, Indranil
10 Castella, Francesc
10 Cullinan, John
10 van der Put, Marius
9 Achter, Jeffrey D.
9 André, Yves
9 Cao, Wei
9 Crew, Richard M.
9 Darmon, Henri René
9 de Shalit, Ehud
9 Dettweiler, Michael
9 Fu, Lei
9 Guerzhoy, Pavel I.
9 Katz, Daniel J.
9 Mazur, Barry
9 Poonen, Bjorn
9 Reiter, Stefan
9 Roques, Julien
9 Ulmer, Douglas L.
9 Zuo, Kang
8 Chen, Imin
8 Coleman, Robert Frederick
8 David, Chantal
8 Evans, Ronald J.
8 Gao, Peng
8 Goren, Eyal Z.
8 Guralnick, Robert Michael
8 Haraoka, Yoshishige
8 Illusie, Luc
8 Kedlaya, Kiran Sridhara
8 Kobayashi, Shinichi
8 Meier, Lennart
8 Pinto dos Santos, João Pedro
8 Soundararajan, Kannan
8 Tilouine, Jacques
8 Voight, John Michael
8 Zarkhin, Yuriĭ Gennad’evich
8 Zhao, Liangyi
7 Andrade, Julio Cesar
7 Berthelot, Pierre
7 Chiarellotto, Bruno
7 Choi, Dohoon
7 Dwork, Bernard Morris
7 Eischen, Ellen Elizabeth
7 Franc, Cameron
7 Hong, Shaofang
7 Hoshi, Yuichiro
7 Howe, Everett W.
7 Kamgarpour, Masoud
7 Kisin, Mark
7 Lauder, Alan G. B.
7 Long, Ling
7 Meisner, Patrick
7 Najman, Filip
7 Phùng Hô‘ Hài
7 Pries, Rachel J.
7 Rivoal, Tanguy
7 Rudnick, Zeév
7 Sarnak, Peter Clive
7 Snaith, Nina Claire
7 Suh, Junecue
7 Templier, Nicolas
7 Voloch, José Felipe
7 Wakabayashi, Yasuhiro
7 Zhang, Wenpeng
6 Andreatta, Fabrizio
6 Bannai, Kenichi
6 Beukers, Frits
6 Blomer, Valentin
6 Böckle, Gebhard
6 Bui, Hung Manh
6 Castro, Francis Noel
6 Chandee, Vorrapan
6 Clark, Peter Louis
6 Cohen, Stephen D.
6 Conrad, Brian
6 Conrey, John Brian
...and 2,191 more Authors
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Cited in 268 Serials

215 Journal of Number Theory
114 Inventiones Mathematicae
103 Compositio Mathematica
95 Duke Mathematical Journal
89 Transactions of the American Mathematical Society
78 Mathematische Annalen
76 Annales de l’Institut Fourier
72 Finite Fields and their Applications
68 Advances in Mathematics
59 Journal of Algebra
51 Mathematische Zeitschrift
48 International Journal of Number Theory
45 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
45 Proceedings of the American Mathematical Society
44 Journal de Théorie des Nombres de Bordeaux
42 Algebra & Number Theory
41 Research in Number Theory
36 Journal für die Reine und Angewandte Mathematik
35 Annals of Mathematics. Second Series
34 Israel Journal of Mathematics
31 Journal of Pure and Applied Algebra
30 Journal of the American Mathematical Society
29 Manuscripta Mathematica
25 Experimental Mathematics
24 Mathematics of Computation
24 The Ramanujan Journal
24 Journal of the Institute of Mathematics of Jussieu
23 Bulletin of the American Mathematical Society. New Series
22 Communications in Mathematical Physics
22 Journal of Algebraic Geometry
22 Documenta Mathematica
21 Comptes Rendus. Mathématique. Académie des Sciences, Paris
20 Selecta Mathematica. New Series
20 Forum of Mathematics, Sigma
19 Research in the Mathematical Sciences
18 Forum Mathematicum
18 Journal of the European Mathematical Society (JEMS)
17 Publications Mathématiques
17 Journal of Symbolic Computation
15 Bulletin de la Société Mathématique de France
15 Proceedings of the London Mathematical Society. Third Series
14 Acta Arithmetica
14 Nagoya Mathematical Journal
14 Publications of the Research Institute for Mathematical Sciences, Kyoto University
14 Rendiconti del Seminario Matematico della Università di Padova
14 Indagationes Mathematicae. New Series
13 Journal of the London Mathematical Society. Second Series
13 European Journal of Mathematics
12 Mathematical Proceedings of the Cambridge Philosophical Society
12 Memoirs of the American Mathematical Society
11 Journal of Mathematical Physics
11 Bulletin of the London Mathematical Society
11 Mathematika
11 Proceedings of the Japan Academy. Series A
11 Geometric and Functional Analysis. GAFA
11 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
10 Communications in Algebra
10 Canadian Journal of Mathematics
10 Functiones et Approximatio. Commentarii Mathematici
10 Monatshefte für Mathematik
10 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
9 Archiv der Mathematik
9 Journal of Soviet Mathematics
9 Mathematische Nachrichten
9 Tôhoku Mathematical Journal. Second Series
9 LMS Journal of Computation and Mathematics
9 Annales Mathématiques du Québec
8 Journal of Geometry and Physics
8 Mémoires de la Société Mathématique de France. Nouvelle Série
8 Algebraic & Geometric Topology
8 Journal of the Australian Mathematical Society
7 Michigan Mathematical Journal
7 Pacific Journal of Mathematics
7 International Journal of Mathematics
7 Oberwolfach Reports
7 Forum of Mathematics, Pi
7 Tunisian Journal of Mathematics
6 Discrete Mathematics
6 Journal of Mathematical Analysis and Applications
6 Mathematical Notes
6 Nuclear Physics. B
6 Journal of Combinatorial Theory. Series A
6 Journal of Differential Equations
6 Japanese Journal of Mathematics. 3rd Series
6 Science China. Mathematics
5 Canadian Mathematical Bulletin
5 Journal of the Mathematical Society of Japan
5 International Journal of Geometric Methods in Modern Physics
5 Cryptography and Communications
5 Kyoto Journal of Mathematics
4 Communications on Pure and Applied Mathematics
4 Journal d’Analyse Mathématique
4 Rocky Mountain Journal of Mathematics
4 Glasgow Mathematical Journal
4 Linear Algebra and its Applications
4 Journal of Mathematical Sciences (New York)
4 Bulletin des Sciences Mathématiques
4 Transformation Groups
4 Representation Theory
4 Milan Journal of Mathematics
...and 168 more Serials
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Cited in 53 Fields

1,722 Number theory (11-XX)
1,369 Algebraic geometry (14-XX)
142 Group theory and generalizations (20-XX)
141 Several complex variables and analytic spaces (32-XX)
137 Field theory and polynomials (12-XX)
127 Special functions (33-XX)
109 Ordinary differential equations (34-XX)
96 Commutative algebra (13-XX)
64 Probability theory and stochastic processes (60-XX)
63 Topological groups, Lie groups (22-XX)
62 Combinatorics (05-XX)
62 Linear and multilinear algebra; matrix theory (15-XX)
56 Algebraic topology (55-XX)
49 Quantum theory (81-XX)
46 \(K\)-theory (19-XX)
39 Category theory; homological algebra (18-XX)
35 Associative rings and algebras (16-XX)
32 Differential geometry (53-XX)
30 Global analysis, analysis on manifolds (58-XX)
29 Computer science (68-XX)
29 Information and communication theory, circuits (94-XX)
28 Dynamical systems and ergodic theory (37-XX)
26 Nonassociative rings and algebras (17-XX)
18 Partial differential equations (35-XX)
18 Manifolds and cell complexes (57-XX)
15 Convex and discrete geometry (52-XX)
15 Statistical mechanics, structure of matter (82-XX)
14 General and overarching topics; collections (00-XX)
13 Functions of a complex variable (30-XX)
13 Difference and functional equations (39-XX)
10 Harmonic analysis on Euclidean spaces (42-XX)
9 History and biography (01-XX)
9 Operator theory (47-XX)
8 Abstract harmonic analysis (43-XX)
7 Mathematical logic and foundations (03-XX)
7 Approximations and expansions (41-XX)
7 Functional analysis (46-XX)
7 Geometry (51-XX)
7 Numerical analysis (65-XX)
6 Integral transforms, operational calculus (44-XX)
5 Measure and integration (28-XX)
4 Real functions (26-XX)
4 Statistics (62-XX)
3 Integral equations (45-XX)
2 Mechanics of particles and systems (70-XX)
2 Relativity and gravitational theory (83-XX)
2 Biology and other natural sciences (92-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Potential theory (31-XX)
1 Sequences, series, summability (40-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Mechanics of deformable solids (74-XX)
1 Operations research, mathematical programming (90-XX)

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