Edit Profile (opens in new tab) Katz, Nicholas Michael Compute Distance To: Compute Author ID: katz.nicholas-m Published as: Katz, Nicholas M.; Katz, N. M.; Katz, Nicholas; Katz, N. Further Spellings: Кац Николас М Homepage: https://web.math.princeton.edu/~nmk/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 140 Publications since 1968, including 9 Books 8 Contributions as Editor · 4 Further Contributions Co-Authors: 40 Co-Authors with 50 Joint Publications 1,428 Co-Co-Authors all top 5 Co-Authors 100 single-authored 12 Tiep Pham Huu 10 Illusie, Luc 9 Laumon, Gérard 7 Cartier, Pierre 7 Ribet, Kenneth Alan 6 Manin, Yuri Ivanovich 4 Rojas-León, Antonio 3 Deligne, Pierre René 2 Berthelot, Pierre 2 Browder, William 2 Fouvry, Etienne 2 Guralnick, Robert Michael 2 Messing, William 2 Oda, Tadao 2 Sarnak, Peter Clive 2 Tate, John Torrence jun. 1 Adolphson, Alan 1 Artin, Michael 1 Atiyah, Michael Francis 1 Baldassarri, Francesco 1 Bass, Hyman 1 Bombieri, Enrico 1 Colliot-Thélène, Jean-Louis 1 de Jong, Aise Johan 1 Demazure, Michel 1 Esnault, Hélène 1 Faltings, Gerd 1 Greenberg, Marvin Jay 1 Harder, Günter 1 Harris, Michael Howard 1 Hartshorne, Robin 1 Hausel, Tamás 1 Iwaniec, Henryk 1 Jackson, Allyn 1 Kleiman, Steven Lawrence 1 Lang, Serge 1 Livné, Ron A. 1 Loeser, François 1 Mazur, Barry 1 Mumford, David Bryant 1 Pandharipande, Rahul 1 Pink, Richard 1 Poonen, Bjorn 1 Rodriguez-Villegas, Fernando 1 Scholze, Peter 1 Shparlinski, Igor E. 1 Voloch, José Felipe 1 Xiong, Maosheng 1 Zheng, Zhiyong all top 5 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 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 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 all top 5 Fields 105 Algebraic geometry (14-XX) 88 Number theory (11-XX) 21 Group theory and generalizations (20-XX) 12 Field theory and polynomials (12-XX) 9 General and overarching topics; collections (00-XX) 7 Commutative algebra (13-XX) 7 Ordinary differential equations (34-XX) 5 History and biography (01-XX) 5 Several complex variables and analytic spaces (32-XX) 3 Combinatorics (05-XX) 2 Topological groups, Lie groups (22-XX) 2 Abstract harmonic analysis (43-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 1 Nonassociative rings and algebras (17-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 133 Publications have been cited 3,033 times in 2,050 Documents Cited by ▼ Year ▼ Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 249 1985 Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004Katz, Nicholas M.; Sarnak, Peter 212 1999 Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin. Zbl 0221.14007Katz, Nicholas M. 198 1970 Gauss sums, Kloosterman sums, and monodromy groups. Zbl 0675.14004Katz, Nicholas M. 153 1988 Exponential sums and differential equations. Zbl 0731.14008Katz, Nicholas M. 125 1990 Zeroes of zeta functions and symmetry. Zbl 0921.11047Katz, Nicholas M.; Sarnak, Peter 124 1999 \(p\)-adic interpolation of real analytic Eisenstein series. Zbl 0354.14007Katz, Nicholas M. 112 1976 Some consequences of the Riemann hypothesis for varieties over finite fields. Zbl 0275.14011Katz, Nicholas M.; Messing, William 108 1974 \(p\)-adic \(L\)-functions for CM fields. Zbl 0417.12003Katz, Nicholas M. 103 1978 Rigid local systems. Zbl 0864.14013Katz, Nicholas M. 89 1996 \(p\)-adic properties of modular schemes and modular forms. Zbl 0271.10033Katz, Nicholas M. 84 1973 Algebraic solutions of differential equations (p-curvature and the Hodge filtration). Zbl 0278.14004Katz, Nicholas M. 78 1972 Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz. Zbl 1213.14020Hausel, Tamás; Rodriguez-Villegas, Fernando 69 2008 Slope filtration of F-crystals. Zbl 0426.14007Katz, Nicholas M. 68 1979 On the differentiation of De Rham cohomology classes with respect to parameters. Zbl 0165.54802Katz, N. M.; Oda, T. 66 1968 On a theorem of Ax. Zbl 0237.12012Katz, Nicholas M. 58 1971 Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.). Zbl 0603.14015Katz, Nicholas M.; Laumon, Gérard 50 1985 Galois properties of torsion points on abelian varieties. Zbl 0471.14023Katz, Nicholas M. 49 1981 On the calculation of some differential Galois groups. Zbl 0609.12025Katz, Nicholas M. 46 1987 Serre-Tate local moduli. Zbl 0477.14007Katz, N. 46 1981 Local-to-global extensions of representations of fundamental groups. Zbl 0564.14013Katz, Nicholas M. 43 1986 Finiteness theorems in geometric classfield theory. (With an appendix by Kenneth A. Ribet). Zbl 0495.14011Katz, Nicholas M.; Lang, Serge 38 1981 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 35 1973 Higher congruences between modular forms. Zbl 0356.10020Katz, Nicholas M. 34 1975 The Eisenstein measure and p-adic interpolation. Zbl 0375.12022Katz, Nicholas M. 27 1977 On the monodromy groups attached to certain families of exponential sums. Zbl 0643.12004Katz, Nicholas M. 26 1987 A conjecture in the arithmetic theory of differential equations. Zbl 0504.12022Katz, Nicholas M. 26 1982 Sums of Betti numbers in arbitrary characteristic. Zbl 1068.14501Katz, Nicholas M. 25 2001 Travaux de Dwork. Zbl 0259.14007Katz, Nicholas 24 1973 Estimates for Soto-Andrade sums. Zbl 0798.11053Katz, Nicholas M. 23 1993 Sommes de Kloosterman et courbes elliptiques universelles en caractéristiques 2 et 3. (Kloosterman sums and universal elliptic curves in characteristics 2 and 3). Zbl 0701.14033Katz, Nicholas; Livné, Ron 22 1989 Moments, monodromy, and perversity. A Diophantine perspective. Zbl 1079.14025Katz, Nicholas M. 21 2005 An estimate for character sums. Zbl 0672.10026Katz, Nicholas M. 20 1989 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050Poonen, Bjorn; Voloch, José Felipe 20 2004 On the differential equations satisfied by period matrices. Zbl 0159.22502Katz, N. M. 20 1968 Estimates for “singular” exponential sums. Zbl 0991.11064Katz, Nicholas M. 18 1999 Sommes exponentielles. Cours à Orsay, automne 1979. Redige par Gerard Laumon, preface par Luc Illusie. Zbl 0469.12007Katz, Nicholas M. 18 1980 A general stratification theorem for exponential sums, and applications. Zbl 0986.11054Fouvry, E.; Katz, N. 18 2001 A simple algorithm for cyclic vectors. Zbl 0621.13003Katz, Nicholas M. 15 1987 Estimates for nonsingular multiplicative character sums. Zbl 1028.11075Katz, Nicholas M. 15 2002 An overview of Deligne’s work on Hilbert’s twenty-first problem. Zbl 0347.14010Katz, Nicholas M. 14 1976 Divisibilities, congruences, and Cartier duality. Zbl 0559.14032Katz, Nicholas M. 14 1981 Exponential sums over finite fields and differential equations over the complex numbers: Some interactions. Zbl 0727.11057Katz, Nicholas M. 13 1990 Pinceaux de Lefschetz: Théoreme d’existence. Zbl 0284.14006Katz, N. M. 12 1973 Convolution and equidistribution. Sato-Tate theorems for finite-field Mellin transforms. Zbl 1261.11084Katz, Nicholas M. 12 2012 Witt vectors and a question of Keating and Rudnick. Zbl 1328.13028Katz, Nicholas M. 12 2013 Another look at the Dwork family. Zbl 1195.14015Katz, Nicholas M. 11 2009 The divisor function over arithmetic progressions. With Appendix by Nicholas Katz. Zbl 0764.11040Fouvry, Etienne; Iwaniec, Henryk 11 1992 Travaux de Laumon. (Works of Laumon). Zbl 0698.14014Katz, Nicholas M. 11 1988 Formal groups and p-adic interpolation. Zbl 0351.14024Katz, Nicholas M. 10 1977 Twisted \(L\)-functions and monodromy. Zbl 1029.14005Katz, Nicholas M. 10 2002 Perversity and exponential sums. Zbl 0755.14008Katz, Nicholas M. 10 1989 Another look at \(p\)-adic \(L\)-functions for totally real fields. Zbl 0497.14006Katz, Nicholas M. 10 1981 Space filling curves over finite fields. Zbl 1016.11022Katz, Nicholas M. 10 2001 \(L\)-functions and monodromy: four lectures on Weil II. Zbl 1016.14011Katz, Nicholas M. 10 2001 The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers. Zbl 0303.10028Katz, Nicholas M. 9 1975 Affine cohomological transforms, perversity, and monodromy. Appendix (d’après Deligne). Zbl 0815.14011Katz, Nicholas M. 9 1993 Factoring polynomials in finite fields: An application of Lang-Weil to a problem in graph theory. Zbl 0708.05029Katz, Nicholas M. 9 1990 p-adic L-functions via moduli of elliptic curves. Zbl 0317.14009Katz, Nicholas M. 9 1975 Larsen’s alternative, moments, and the monodromy of Lefschetz pencils. Zbl 1081.14015Katz, Nicholas M. 8 2004 Crystalline cohomology, Dieudonne modules, and Jacobi sums. Zbl 0502.14007Katz, Nicholas M. 8 1981 Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess. Zbl 1023.11031Katz, Nicholas M. 8 2001 Une formule de congruence pour la fonction \(\zeta\). Zbl 0275.14015Katz, N. 8 1973 Étude cohomologique des pinceaux de Lefschetz. Zbl 0284.14007Katz, N. 8 1973 Notes on \(G_{2}\), determinants, and equidistribution. Zbl 1065.11060Katz, Nicholas M. 8 2004 Rigid local systems on \(\mathbb{A}^{1}\) with finite monodromy. Zbl 1456.11232Katz, Nicholas M. 8 2018 On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor. Zbl 1358.11127Katz, Nicholas M. 8 2013 Review of \(\ell\)-adic cohomology. Zbl 0817.14006Katz, Nicholas M. 7 1994 The regularity theorem in algebraic geometry. Zbl 0235.14006Katz, Nicholas M. 7 1971 \(G_2\) and hypergeometric sheaves. Zbl 1167.14013Katz, Nicholas M. 7 2007 A semicontinuity result for monodromy under degeneration. Zbl 1070.14024Katz, Nicholas M. 6 2003 Internal reconstruction of unit-root F-crystals via expansion- coefficients. Appendix: ”Some results on partial Hodge-Witt decompositions” by Luc Illusie. Zbl 0592.14021Katz, Nicholas M. 6 1985 A result on modular forms in characteristic p. Zbl 0392.10026Katz, Nicholas M. 6 1977 Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families. Zbl 1067.14504de Jong, A. Johan; Katz, Nicholas M. 6 2000 On the intersection matrix of a hypersurface. Zbl 0187.42802Katz, Nicholas M. 6 1969 A note on lower bounds for Frobenius traces. Zbl 1220.11078Bombieri, Enrico; Katz, Nicholas M. 6 2010 Corrections to: A conjecture in the arithmetic theory of differential equations. Zbl 0513.12018Katz, Nicholas M. 5 1982 On the uniform distribution of Gauss sums and Jacobi sums. Zbl 0866.11073Katz, Nicholas M.; Zheng, Zhiyong 5 1996 Lang-Trotter revisited. Zbl 1234.11072Katz, Nicholas M. 5 2009 A rigid local system with monodromy group \(2.J_{2}\). Zbl 1467.11115Katz, Nicholas M.; Rojas-León, Antonio 5 2019 Rigid local systems and alternating groups. Zbl 1454.11217Guralnick, Robert; Katz, Nicholas; Tiep, Pham Huu 5 2019 A note on exponential sums. Zbl 0851.11073Katz, Nicholas M. 4 1995 A note on pseudo-CM representations and differential Galois groups. Zbl 0643.12007Katz, Nicholas M.; Pink, Richard 4 1987 From Clausen to Carlitz: low-dimensional spin groups and identities among character sums. Zbl 1234.11103Katz, Nicholas M. 4 2009 Estimates for nonsingular mixed character sums. Zbl 1145.11084Katz, Nicholas M. 4 2007 Rigid local systems and a question of Wootters. Zbl 1368.11131Katz, Nicholas M. 4 2012 Introduction aux travaux récents de Dwork. Zbl 0218.14011Katz, N. M. 4 1971 Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\). Zbl 1446.11210Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 4 2020 Rigid local systems and finite symplectic groups. Zbl 1459.11225Katz, Nicholas M.; Tiep, Pham Huu 4 2019 Elliptic convolution, \(G_2\), and elliptic surfaces. Zbl 1326.14017Katz, Nicholas M. 4 2015 Sato-Tate in the higher dimensional case: elaboration of 9.5.4 in Serre’s \(N_X(p)\) book. Zbl 1320.14042Katz, Nicholas M. 4 2013 Wild ramification and some problems of ”independence of \(\ell ''\). Zbl 0568.14012Katz, Nicholas M. 3 1983 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 1457.11169Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 3 2020 Wieferich past and future. Zbl 1416.11082Katz, Nicholas M. 3 2015 On a question of Lillian Pierce. Zbl 1139.11055Katz, Nicholas M. 3 2006 Local systems and finite unitary and symplectic groups. Zbl 1425.14009Katz, Nicholas M.; Tiep, Pham Huu 3 2019 Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_2\). Zbl 1460.11144Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 3 2020 Witt vectors and a question of Rudnick and Waxman. Zbl 1405.13040Katz, Nicholas M. 3 2017 Automorphic realization of residual Galois representations. Zbl 1257.11051Guralnick, Robert; Harris, Michael; Katz, Nicholas M. 2 2010 An overview of Deligne’s proof of the Riemann hypothesis for varieties over finite fields. Zbl 0339.14013Katz, Nicholas M. 2 1976 Rigid local systems and finite general linear groups. Zbl 07373918Katz, Nicholas M.; Tiep, Pham Huu 1 2021 Exponential sums and total Weil representations of finite symplectic and unitary groups. Zbl 07390619Katz, Nicholas M.; Tiep, Pham Huu 1 2021 Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\). Zbl 1446.11210Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 4 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 1457.11169Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 3 2020 Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_2\). Zbl 1460.11144Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 3 2020 Moments of Weil representations of finite special unitary groups. Zbl 07239067Katz, Nicholas M.; Tiep, Pham Huu 1 2020 A rigid local system with monodromy group \(2.J_{2}\). Zbl 1467.11115Katz, Nicholas M.; Rojas-León, Antonio 5 2019 Rigid local systems and alternating groups. Zbl 1454.11217Guralnick, Robert; Katz, Nicholas; Tiep, Pham Huu 5 2019 Rigid local systems and finite symplectic groups. Zbl 1459.11225Katz, Nicholas M.; Tiep, Pham Huu 4 2019 Local systems and finite unitary and symplectic groups. Zbl 1425.14009Katz, Nicholas M.; Tiep, Pham Huu 3 2019 Rigid local systems on \(\mathbb{A}^{1}\) with finite monodromy. Zbl 1456.11232Katz, Nicholas M. 8 2018 Witt vectors and a question of Rudnick and Waxman. Zbl 1405.13040Katz, Nicholas M. 3 2017 \(G_{2}\) and some exceptional Witt vector identities. Zbl 1409.11131Katz, Nicholas M. 1 2017 A note on random matrix integrals, moment identities, and Catalan numbers. Zbl 1350.22009Katz, Nicholas M. 2 2016 Alexandre Grothendieck 1928–2014. I. Zbl 1338.01022Atiyah, Michael; Bass, Hyman; Cartier, Pierre; Deligne, Pierre; Demazure, Michel; Greenberg, Marvin Jay; Hartshorne, Robin; Illusie, Luc; Katz, Nicholas; Kleiman, Steven L. 1 2016 Elliptic convolution, \(G_2\), and elliptic surfaces. Zbl 1326.14017Katz, Nicholas M. 4 2015 Wieferich past and future. Zbl 1416.11082Katz, Nicholas M. 3 2015 On two questions of Entin, Keating, and Rudnick on primitive Dirichlet characters. Zbl 1385.11072Katz, Nicholas M. 1 2015 Witt vectors and a question of Entin, Keating, and Rudnick. Zbl 1346.13045Katz, Nicholas M. 1 2015 On a question of Rudnick: do we have square root cancellation for error terms in moment calculations? Zbl 1386.11094Katz, Nicholas M. 1 2015 Witt vectors and a question of Keating and Rudnick. Zbl 1328.13028Katz, Nicholas M. 12 2013 On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor. Zbl 1358.11127Katz, Nicholas M. 8 2013 Sato-Tate in the higher dimensional case: elaboration of 9.5.4 in Serre’s \(N_X(p)\) book. Zbl 1320.14042Katz, Nicholas M. 4 2013 Convolution and equidistribution. Sato-Tate theorems for finite-field Mellin transforms. Zbl 1261.11084Katz, Nicholas M. 12 2012 Rigid local systems and a question of Wootters. Zbl 1368.11131Katz, Nicholas M. 4 2012 Report on the irreducibility of \(L\)-functions. Zbl 1276.11147Katz, Nicholas M. 2 2012 A note on lower bounds for Frobenius traces. Zbl 1220.11078Bombieri, Enrico; Katz, Nicholas M. 6 2010 Automorphic realization of residual Galois representations. Zbl 1257.11051Guralnick, Robert; Harris, Michael; Katz, Nicholas M. 2 2010 2, 3, 5, Legendre: \(\pm \) trace ratios in families of elliptic curves. Zbl 1295.14026Katz, Nicholas M. 1 2010 Another look at the Dwork family. Zbl 1195.14015Katz, Nicholas M. 11 2009 Lang-Trotter revisited. Zbl 1234.11072Katz, Nicholas M. 5 2009 From Clausen to Carlitz: low-dimensional spin groups and identities among character sums. Zbl 1234.11103Katz, Nicholas M. 4 2009 On a question of Browning and Heath-Brown. Zbl 1253.11080Katz, Nicholas M. 2 2009 On character sums with distances on the upper half plane over a finite field. Zbl 1253.11109Katz, Nicholas M.; Shparlinski, Igor E.; Xiong, Maosheng 1 2009 Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz. Zbl 1213.14020Hausel, Tamás; Rodriguez-Villegas, Fernando 69 2008 Estimates for mixed character sums. Zbl 1226.11129Katz, Nicholas M. 1 2008 \(G_2\) and hypergeometric sheaves. Zbl 1167.14013Katz, Nicholas M. 7 2007 Estimates for nonsingular mixed character sums. Zbl 1145.11084Katz, Nicholas M. 4 2007 On a question of Lillian Pierce. Zbl 1139.11055Katz, Nicholas M. 3 2006 Moments, monodromy, and perversity. A Diophantine perspective. Zbl 1079.14025Katz, Nicholas M. 21 2005 Cohomological divisibility and point count divisibility. Zbl 1076.14028Esnault, Hélène; Katz, Nicholas M. 1 2005 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050Poonen, Bjorn; Voloch, José Felipe 20 2004 Larsen’s alternative, moments, and the monodromy of Lefschetz pencils. Zbl 1081.14015Katz, Nicholas M. 8 2004 Notes on \(G_{2}\), determinants, and equidistribution. Zbl 1065.11060Katz, Nicholas M. 8 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 1092.14016Katz, Nicholas M.; Pandharipande, Rahul 1 2004 A semicontinuity result for monodromy under degeneration. Zbl 1070.14024Katz, Nicholas M. 6 2003 Estimates for nonsingular multiplicative character sums. Zbl 1028.11075Katz, Nicholas M. 15 2002 Twisted \(L\)-functions and monodromy. Zbl 1029.14005Katz, Nicholas M. 10 2002 Sums of Betti numbers in arbitrary characteristic. Zbl 1068.14501Katz, Nicholas M. 25 2001 A general stratification theorem for exponential sums, and applications. Zbl 0986.11054Fouvry, E.; Katz, N. 18 2001 Space filling curves over finite fields. Zbl 1016.11022Katz, Nicholas M. 10 2001 \(L\)-functions and monodromy: four lectures on Weil II. Zbl 1016.14011Katz, Nicholas M. 10 2001 Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess. Zbl 1023.11031Katz, Nicholas M. 8 2001 Sato-Tate equidistribution of Kurlberg-Rudnick sums. Zbl 1011.11058Katz, Nicholas M. 1 2001 Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families. Zbl 1067.14504de Jong, A. Johan; Katz, Nicholas M. 6 2000 Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004Katz, Nicholas M.; Sarnak, Peter 212 1999 Zeroes of zeta functions and symmetry. Zbl 0921.11047Katz, Nicholas M.; Sarnak, Peter 124 1999 Estimates for “singular” exponential sums. Zbl 0991.11064Katz, Nicholas M. 18 1999 Bernard Dwork (1923–1998). Zbl 1177.01050Katz, Nicholas M.; Tate, John 1 1999 Rigid local systems. Zbl 0864.14013Katz, Nicholas M. 89 1996 On the uniform distribution of Gauss sums and Jacobi sums. Zbl 0866.11073Katz, Nicholas M.; Zheng, Zhiyong 5 1996 A note on exponential sums. Zbl 0851.11073Katz, Nicholas M. 4 1995 Review of \(\ell\)-adic cohomology. Zbl 0817.14006Katz, Nicholas M. 7 1994 Perversity and exponential sums. II: Estimates for and inequalities among \(A\)-numbers. Zbl 0837.14017Katz, Nicholas M. 2 1994 Independence of \(\ell\) and weak Lefschetz. Zbl 0813.14013Katz, Nicholas M. 1 1994 Estimates for Soto-Andrade sums. Zbl 0798.11053Katz, Nicholas M. 23 1993 Affine cohomological transforms, perversity, and monodromy. Appendix (d’après Deligne). Zbl 0815.14011Katz, Nicholas M. 9 1993 The divisor function over arithmetic progressions. With Appendix by Nicholas Katz. Zbl 0764.11040Fouvry, Etienne; Iwaniec, Henryk 11 1992 Exponential sums and differential equations. Zbl 0731.14008Katz, Nicholas M. 125 1990 Exponential sums over finite fields and differential equations over the complex numbers: Some interactions. Zbl 0727.11057Katz, Nicholas M. 13 1990 Factoring polynomials in finite fields: An application of Lang-Weil to a problem in graph theory. Zbl 0708.05029Katz, 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 2 1990 The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume II. Zbl 0717.00009 1 1990 Sommes de Kloosterman et courbes elliptiques universelles en caractéristiques 2 et 3. (Kloosterman sums and universal elliptic curves in characteristics 2 and 3). Zbl 0701.14033Katz, Nicholas; Livné, Ron 22 1989 An estimate for character sums. Zbl 0672.10026Katz, Nicholas M. 20 1989 Perversity and exponential sums. Zbl 0755.14008Katz, Nicholas M. 10 1989 Corrections à: “Transformation de Fourier et majoration de sommes exponentielles”. (Corrections to: “Fourier transformation and majorization of exponential sums”). Zbl 0705.14020Katz, Nicholas M.; Laumon, Gérard 2 1989 Gauss sums, Kloosterman sums, and monodromy groups. Zbl 0675.14004Katz, Nicholas M. 153 1988 Travaux de Laumon. (Works of Laumon). Zbl 0698.14014Katz, Nicholas M. 11 1988 On the calculation of some differential Galois groups. Zbl 0609.12025Katz, Nicholas M. 46 1987 On the monodromy groups attached to certain families of exponential sums. Zbl 0643.12004Katz, Nicholas M. 26 1987 A simple algorithm for cyclic vectors. Zbl 0621.13003Katz, Nicholas M. 15 1987 A note on pseudo-CM representations and differential Galois groups. Zbl 0643.12007Katz, Nicholas M.; Pink, Richard 4 1987 On a certain class of exponential sums. Zbl 0604.12015Katz, Nicholas M. 1 1987 Local-to-global extensions of representations of fundamental groups. Zbl 0564.14013Katz, Nicholas M. 43 1986 Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 249 1985 Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.). Zbl 0603.14015Katz, Nicholas M.; Laumon, Gérard 50 1985 Internal reconstruction of unit-root F-crystals via expansion- coefficients. Appendix: ”Some results on partial Hodge-Witt decompositions” by Luc Illusie. Zbl 0592.14021Katz, Nicholas M. 6 1985 Wild ramification and some problems of ”independence of \(\ell ''\). Zbl 0568.14012Katz, Nicholas M. 3 1983 A conjecture in the arithmetic theory of differential equations. Zbl 0504.12022Katz, Nicholas M. 26 1982 Corrections to: A conjecture in the arithmetic theory of differential equations. Zbl 0513.12018Katz, Nicholas M. 5 1982 Free actions of finite groups on varieties. II. Zbl 0551.14019Browder, William; Katz, Nicholas M. 2 1982 Free actions of finite groups on varieties. I. Zbl 0551.57022Browder, William; Katz, Nicholas M. 1 1982 Galois properties of torsion points on abelian varieties. Zbl 0471.14023Katz, Nicholas M. 49 1981 Serre-Tate local moduli. Zbl 0477.14007Katz, N. 46 1981 Finiteness theorems in geometric classfield theory. (With an appendix by Kenneth A. Ribet). Zbl 0495.14011Katz, Nicholas M.; Lang, Serge 38 1981 Divisibilities, congruences, and Cartier duality. Zbl 0559.14032Katz, Nicholas M. 14 1981 Another look at \(p\)-adic \(L\)-functions for totally real fields. Zbl 0497.14006Katz, Nicholas M. 10 1981 Crystalline cohomology, Dieudonne modules, and Jacobi sums. Zbl 0502.14007Katz, Nicholas M. 8 1981 ...and 33 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,774 Authors 45 Katz, Nicholas Michael 30 Shparlinski, Igor E. 21 Hida, Haruzo 19 Sperber, Steven I. 17 Kowalski, Emmanuel 17 Wan, Daqing 16 Michel, Philippe Gabriel 16 Miller, Steven J. 15 Tiep Pham Huu 14 Adolphson, Alan 14 Fouvry, Etienne 12 Gross, Benedict Hyman 12 Harris, Michael Howard 12 Panchishkin, Alexei A. 12 Rojas-León, Antonio 12 Sawin, William F. 12 Zaharescu, Alexandru 11 Esnault, Hélène 11 Keating, Jonathan Peter 10 van der Put, Marius 9 André, Yves 9 Barman, Rupam 9 Buium, Alexandru 9 Burungale, Ashay A. 9 Dettweiler, Michael 9 Katz, Daniel J. 9 Mazur, Barry 9 Poonen, Bjorn 9 Reiter, Stefan 8 Achter, Jeffrey D. 8 Coleman, Robert Frederick 8 Crew, Richard M. 8 Darmon, Henri René 8 Fu, Lei 8 Roques, Julien 8 Tilouine, Jacques 8 Xi, Ping 7 Andrade, Julio Cesar 7 Biswas, Indranil 7 Cao, Wei 7 Chiarellotto, Bruno 7 Cullinan, John 7 de Shalit, Ehud 7 Dwork, Bernard Morris 7 Evans, Ronald J. 7 Guerzhoy, Pavel I. 7 Guralnick, Robert Michael 7 Illusie, Luc 7 Rudnick, Zeév 7 Sarnak, Peter Clive 7 Snaith, Nina Claire 7 Ulmer, Douglas L. 7 Voloch, José Felipe 6 Berthelot, Pierre 6 Böckle, Gebhard 6 Castella, Francesc 6 Castro, Francis Noel 6 Chen, Imin 6 Cohen, Stephen D. 6 Conrad, Brian 6 David, Chantal 6 Eischen, Ellen Elizabeth 6 Etesse, Jean-Yves 6 Goren, Eyal Z. 6 Haraoka, Yoshishige 6 Hong, Shaofang 6 Kedlaya, Kiran Sridhara 6 Kobayashi, Shinichi 6 Lauder, Alan G. B. 6 Pink, Richard 6 Pries, Rachel J. 6 Rubinstein, Michael O. 6 Suh, Junecue 6 Zarkhin, Yuriĭ Gennad’evich 6 Zuo, Kang 5 Andreatta, Fabrizio 5 Baldassarri, Francesco 5 Beukers, Frits 5 Chandee, Vorrapan 5 Clark, Peter Louis 5 Forrester, Peter J. 5 Goss, David Mark 5 Gros, Michel 5 Hall, Chris 5 Hoshi, Yuichiro 5 Hsieh, Ming-Lun 5 Kerz, Moritz C. 5 Kisin, Mark 5 Lachaud, Gilles 5 Lan, Kai-Wen 5 Langevin, Philippe 5 Larsen, Michael Jeffrey 5 Long, Ling 5 Meier, Lennart 5 Milne, James Stuart 5 Movasati, Hossein 5 Ogus, Arthur 5 Oort, Frans 5 Roditty-Gershon, Edva 5 Rotger, Victor ...and 1,674 more Authors all top 5 Cited in 225 Serials 170 Journal of Number Theory 104 Inventiones Mathematicae 88 Duke Mathematical Journal 87 Compositio Mathematica 70 Annales de l’Institut Fourier 66 Transactions of the American Mathematical Society 63 Mathematische Annalen 58 Finite Fields and their Applications 55 Advances in Mathematics 48 Journal of Algebra 42 Proceedings of the American Mathematical Society 41 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 41 Mathematische Zeitschrift 41 International Journal of Number Theory 36 Journal de Théorie des Nombres de Bordeaux 31 Israel Journal of Mathematics 28 Annals of Mathematics. Second Series 27 Journal of the American Mathematical Society 25 Manuscripta Mathematica 24 Journal für die Reine und Angewandte Mathematik 21 Journal of Pure and Applied Algebra 21 Bulletin of the American Mathematical Society. New Series 21 Research in Number Theory 20 Mathematics of Computation 19 Communications in Mathematical Physics 19 Journal of Algebraic Geometry 17 Experimental Mathematics 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Journal of the Institute of Mathematics of Jussieu 16 Forum of Mathematics, Sigma 15 Publications Mathématiques 15 Selecta Mathematica. New Series 15 Documenta Mathematica 15 The Ramanujan Journal 15 Algebra & Number Theory 14 Research in the Mathematical Sciences 13 Publications of the Research Institute for Mathematical Sciences, Kyoto University 13 Journal of Symbolic Computation 13 Forum Mathematicum 12 Rendiconti del Seminario Matematico della Università di Padova 12 Journal of the European Mathematical Society (JEMS) 11 Geometric and Functional Analysis. GAFA 11 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Journal of Mathematical Physics 10 Nagoya Mathematical Journal 10 Proceedings of the Japan Academy. Series A 10 Indagationes Mathematicae. New Series 9 Mathematical Proceedings of the Cambridge Philosophical Society 9 Acta Arithmetica 9 Journal of Soviet Mathematics 9 LMS Journal of Computation and Mathematics 8 Archiv der Mathematik 8 Bulletin de la Société Mathématique de France 8 Tohoku Mathematical Journal. Second Series 8 Mémoires de la Société Mathématique de France. Nouvelle Série 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 7 Journal of Geometry and Physics 7 Functiones et Approximatio. Commentarii Mathematici 7 Mathematika 7 Monatshefte für Mathematik 7 Algebraic & Geometric Topology 6 International Journal of Mathematics 6 Journal of the Australian Mathematical Society 6 Japanese Journal of Mathematics. 3rd Series 6 European Journal of Mathematics 5 Communications in Algebra 5 Discrete Mathematics 5 Journal of Mathematical Analysis and Applications 5 Canadian Journal of Mathematics 5 Journal of Combinatorial Theory. Series A 5 Journal of Differential Equations 5 Mathematische Nachrichten 5 Memoirs of the American Mathematical Society 5 Michigan Mathematical Journal 5 Forum of Mathematics, Pi 5 Annales Mathématiques du Québec 4 Communications on Pure and Applied Mathematics 4 Mathematical Notes 4 Nuclear Physics. B 4 Rocky Mountain Journal of Mathematics 4 Journal of the Mathematical Society of Japan 4 Pacific Journal of Mathematics 4 Transformation Groups 4 Representation Theory 4 Milan Journal of Mathematics 4 International Journal of Geometric Methods in Modern Physics 4 Cryptography and Communications 4 Science China. Mathematics 3 Bulletin of the Australian Mathematical Society 3 Discrete Applied Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 The Annals of Probability 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Canadian Mathematical Bulletin 3 Glasgow Mathematical Journal 3 Osaka Journal of Mathematics 3 Theoretical Computer Science 3 Chinese Annals of Mathematics. Series B 3 Designs, Codes and Cryptography 3 Applicable Algebra in Engineering, Communication and Computing ...and 125 more Serials all top 5 Cited in 50 Fields 1,280 Number theory (11-XX) 1,048 Algebraic geometry (14-XX) 122 Field theory and polynomials (12-XX) 108 Group theory and generalizations (20-XX) 106 Several complex variables and analytic spaces (32-XX) 91 Special functions (33-XX) 89 Ordinary differential equations (34-XX) 72 Commutative algebra (13-XX) 51 Combinatorics (05-XX) 50 Linear and multilinear algebra; matrix theory (15-XX) 47 Topological groups, Lie groups (22-XX) 47 Probability theory and stochastic processes (60-XX) 42 Algebraic topology (55-XX) 35 Quantum theory (81-XX) 32 \(K\)-theory (19-XX) 29 Category theory; homological algebra (18-XX) 26 Computer science (68-XX) 25 Associative rings and algebras (16-XX) 25 Global analysis, analysis on manifolds (58-XX) 25 Information and communication theory, circuits (94-XX) 23 Dynamical systems and ergodic theory (37-XX) 19 Differential geometry (53-XX) 18 Nonassociative rings and algebras (17-XX) 15 Partial differential equations (35-XX) 14 Statistical mechanics, structure of matter (82-XX) 12 Manifolds and cell complexes (57-XX) 9 General and overarching topics; collections (00-XX) 9 Functions of a complex variable (30-XX) 9 Difference and functional equations (39-XX) 7 Operator theory (47-XX) 7 Convex and discrete geometry (52-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Abstract harmonic analysis (43-XX) 6 Functional analysis (46-XX) 5 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 5 Approximations and expansions (41-XX) 5 Geometry (51-XX) 5 Numerical analysis (65-XX) 4 Integral transforms, operational calculus (44-XX) 3 Measure and integration (28-XX) 3 Statistics (62-XX) 2 Integral equations (45-XX) 2 Relativity and gravitational theory (83-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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