Edit Profile Katz, Nicholas Michael Compute Distance To: Compute Author ID: katz.nicholas-m Published as: Katz, N.; Katz, N. M.; Katz, Nicholas; Katz, Nicholas M. Homepage: https://web.math.princeton.edu/~nmk/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND Documents Indexed: 143 Publications since 1968, including 16 Books all top 5 Co-Authors 103 single-authored 8 Illusie, Luc 8 Laumon, Gérard 7 Cartier, Pierre 7 Tiep Pham Huu 6 Manin, Yuri Ivanovich 6 Ribet, Kenneth Alan 4 Rojas-León, Antonio 2 Berthelot, Pierre 2 Browder, William 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 de Jong, Aise Johan 1 Deligne, Pierre René 1 Demazure, Michel 1 Esnault, Hélène 1 Faltings, Gerd 1 Fouvry, Etienne 1 Greenberg, Marvin Jay 1 Harder, Günter 1 Harris, Michael Howard 1 Hartshorne, Robin 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 Scholze, Peter 1 Shparlinski, Igor E. 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 5 Inventiones Mathematicae 4 American Journal of Mathematics 4 Publications Mathématiques 4 Mathematische Annalen 4 L’Enseignement Mathématique. 2e Série 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 Experimental Mathematics 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 Annals of Mathematics. Second Series 1 Israel Journal of Mathematics 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 Transactions of the American Mathematical Society 1 Geometric and Functional Analysis. GAFA 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 Communications in Number Theory and Physics 1 Philosophical Transactions A. Royal Society of London 1 Tunisian Journal of Mathematics all top 5 Fields 101 Algebraic geometry (14-XX) 81 Number theory (11-XX) 17 Group theory and generalizations (20-XX) 12 Field theory and polynomials (12-XX) 8 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 124 Publications have been cited 2,720 times in 1,943 Documents Cited by ▼ Year ▼ Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 236 1985 Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004Katz, Nicholas M.; Sarnak, Peter 205 1999 Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin. Zbl 0221.14007Katz, Nicholas M. 188 1970 Gauss sums, Kloosterman sums, and monodromy groups. Zbl 0675.14004Katz, Nicholas M. 144 1988 Zeroes of zeta functions and symmetry. Zbl 0921.11047Katz, Nicholas M.; Sarnak, Peter 119 1999 Exponential sums and differential equations. Zbl 0731.14008Katz, Nicholas M. 112 1990 Some consequences of the Riemann hypothesis for varieties over finite fields. Zbl 0275.14011Katz, Nicholas M.; Messing, William 105 1974 \(p\)-adic interpolation of real analytic Eisenstein series. Zbl 0354.14007Katz, Nicholas M. 104 1976 \(p\)-adic \(L\)-functions for CM fields. Zbl 0417.12003Katz, Nicholas M. 92 1978 \(p\)-adic properties of modular schemes and modular forms. Zbl 0271.10033Katz, Nicholas M. 89 1973 Rigid local systems. Zbl 0864.14013Katz, Nicholas M. 86 1996 Algebraic solutions of differential equations (p-curvature and the Hodge filtration). Zbl 0278.14004Katz, Nicholas M. 72 1972 Slope filtration of F-crystals. Zbl 0426.14007Katz, Nicholas M. 65 1979 On the differentiation of De Rham cohomology classes with respect to parameters. Zbl 0165.54802Katz, N. M.; Oda, T. 61 1968 On a theorem of Ax. Zbl 0237.12012Katz, Nicholas M. 51 1971 Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.). Zbl 0603.14015Katz, Nicholas M.; Laumon, Gérard 47 1985 On the calculation of some differential Galois groups. Zbl 0609.12025Katz, Nicholas M. 44 1987 Galois properties of torsion points on abelian varieties. Zbl 0471.14023Katz, Nicholas M. 42 1981 Serre-Tate local moduli. Zbl 0477.14007Katz, N. 41 1981 Local-to-global extensions of representations of fundamental groups. Zbl 0564.14013Katz, Nicholas M. 39 1986 Finiteness theorems in geometric classfield theory. (With an appendix by Kenneth A. Ribet). Zbl 0495.14011Katz, Nicholas M.; Lang, Serge 34 1981 Higher congruences between modular forms. Zbl 0356.10020Katz, Nicholas M. 31 1975 A conjecture in the arithmetic theory of differential equations. Zbl 0504.12022Katz, Nicholas M. 26 1982 The Eisenstein measure and p-adic interpolation. Zbl 0375.12022Katz, Nicholas M. 26 1977 Travaux de Dwork. Zbl 0259.14007Katz, Nicholas 26 1973 On the monodromy groups attached to certain families of exponential sums. Zbl 0643.12004Katz, Nicholas M. 24 1987 Estimates for Soto-Andrade sums. Zbl 0798.11053Katz, Nicholas M. 22 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 21 1989 Sums of Betti numbers in arbitrary characteristic. Zbl 1068.14501Katz, Nicholas M. 20 2001 Sommes exponentielles. Cours à Orsay, automne 1979. Redige par Gerard Laumon, preface par Luc Illusie. Zbl 0469.12007Katz, Nicholas M. 20 1980 Moments, monodromy, and perversity. A Diophantine perspective. Zbl 1079.14025Katz, Nicholas M. 19 2005 An estimate for character sums. Zbl 0672.10026Katz, Nicholas M. 19 1989 On the differential equations satisfied by period matrices. Zbl 0159.22502Katz, N. M. 19 1968 A general stratification theorem for exponential sums, and applications. Zbl 0986.11054Fouvry, E.; Katz, N. 17 2001 Estimates for “singular” exponential sums. Zbl 0991.11064Katz, Nicholas M. 16 1999 A simple algorithm for cyclic vectors. Zbl 0621.13003Katz, Nicholas M. 15 1987 An overview of Deligne’s work on Hilbert’s twenty-first problem. Zbl 0347.14010Katz, Nicholas M. 15 1976 Estimates for nonsingular multiplicative character sums. Zbl 1028.11075Katz, Nicholas M. 14 2002 p-adic L-functions via moduli of elliptic curves. Zbl 0317.14009Katz, Nicholas M. 14 1975 Exponential sums over finite fields and differential equations over the complex numbers: Some interactions. Zbl 0727.11057Katz, Nicholas M. 13 1990 Divisibilities, congruences, and Cartier duality. Zbl 0559.14032Katz, Nicholas M. 13 1981 Pinceaux de Lefschetz: Théoreme d’existence. Zbl 0284.14006Katz, N. M. 13 1973 Another look at the Dwork family. Zbl 1195.14015Katz, Nicholas M. 11 2009 Twisted \(L\)-functions and monodromy. Zbl 1029.14005Katz, Nicholas M. 11 2002 Convolution and equidistribution. Sato-Tate theorems for finite-field Mellin transforms. Zbl 1261.11084Katz, Nicholas M. 10 2012 Space filling curves over finite fields. Zbl 1016.11022Katz, Nicholas M. 10 2001 Another look at \(p\)-adic \(L\)-functions for totally real fields. Zbl 0497.14006Katz, Nicholas M. 10 1981 Formal groups and p-adic interpolation. Zbl 0351.14024Katz, Nicholas M. 10 1977 Witt vectors and a question of Keating and Rudnick. Zbl 1328.13028Katz, Nicholas M. 9 2013 \(L\)-functions and monodromy: four lectures on Weil II. Zbl 1016.14011Katz, Nicholas M. 9 2001 Factoring polynomials in finite fields: An application of Lang-Weil to a problem in graph theory. Zbl 0708.05029Katz, Nicholas M. 9 1990 Travaux de Laumon. (Works of Laumon). Zbl 0698.14014Katz, Nicholas M. 9 1988 The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers. Zbl 0303.10028Katz, Nicholas M. 9 1975 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 Frobenius-Schur indicator and the ubiquity of Brock-Granville quadratic excess. Zbl 1023.11031Katz, Nicholas M. 8 2001 Affine cohomological transforms, perversity, and monodromy. Appendix (d’après Deligne). Zbl 0815.14011Katz, Nicholas M. 8 1993 Perversity and exponential sums. Zbl 0755.14008Katz, Nicholas M. 8 1989 Crystalline cohomology, Dieudonne modules, and Jacobi sums. Zbl 0502.14007Katz, Nicholas M. 8 1981 Étude cohomologique des pinceaux de Lefschetz. Zbl 0284.14007Katz, N. 8 1973 Une formule de congruence pour la fonction \(\zeta\). Zbl 0275.14015Katz, N. 8 1973 The regularity theorem in algebraic geometry. Zbl 0235.14006Katz, Nicholas M. 8 1971 Rigid local systems on \(\mathbb{A}^{1}\) with finite monodromy. Zbl 1456.11232Katz, Nicholas M. 7 2018 \(G_2\) and hypergeometric sheaves. Zbl 1167.14013Katz, Nicholas M. 7 2007 Review of \(\ell\)-adic cohomology. Zbl 0817.14006Katz, Nicholas M. 7 1994 On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor. Zbl 1358.11127Katz, Nicholas M. 6 2013 Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families. Zbl 1067.14504de Jong, A. Johan; Katz, Nicholas M. 6 2000 A result on modular forms in characteristic p. Zbl 0392.10026Katz, Nicholas M. 6 1977 Lang-Trotter revisited. Zbl 1234.11072Katz, Nicholas M. 5 2009 A semicontinuity result for monodromy under degeneration. Zbl 1070.14024Katz, Nicholas M. 5 2003 On the uniform distribution of Gauss sums and Jacobi sums. Zbl 0866.11073Katz, Nicholas M.; Zheng, Zhiyong 5 1996 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. 5 1985 On the intersection matrix of a hypersurface. Zbl 0187.42802Katz, Nicholas M. 5 1969 Rigid local systems and alternating groups. Zbl 1454.11217Guralnick, Robert; Katz, Nicholas; Tiep, Pham Huu 4 2019 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 Rigid local systems and a question of Wootters. Zbl 1368.11131Katz, Nicholas M. 4 2012 Estimates for nonsingular mixed character sums. Zbl 1145.11084Katz, Nicholas M. 4 2007 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 Corrections to: A conjecture in the arithmetic theory of differential equations. Zbl 0513.12018Katz, Nicholas M. 4 1982 Introduction aux travaux récents de Dwork. Zbl 0218.14011Katz, N. M. 4 1971 A rigid local system with monodromy group \(2.J_{2}\). Zbl 07067789Katz, Nicholas M.; Rojas-León, Antonio 3 2019 Wieferich past and future. Zbl 1416.11082Katz, Nicholas M. 3 2015 A note on lower bounds for Frobenius traces. Zbl 1220.11078Bombieri, Enrico; Katz, Nicholas M. 3 2010 On a question of Lillian Pierce. Zbl 1139.11055Katz, Nicholas M. 3 2006 Wild ramification and some problems of ”independence of \(\ell ''\). Zbl 0568.14012Katz, Nicholas M. 3 1983 An overview of Deligne’s proof of the Riemann hypothesis for varieties over finite fields. Zbl 0339.14013Katz, Nicholas M. 3 1976 Rigid local systems and finite symplectic groups. Zbl 1459.11225Katz, Nicholas M.; Tiep, Pham Huu 2 2019 Witt vectors and a question of Rudnick and Waxman. Zbl 1405.13040Katz, Nicholas M. 2 2017 A note on random matrix integrals, moment identities, and Catalan numbers. Zbl 1350.22009Katz, Nicholas M. 2 2016 Elliptic convolution, \(G_2\), and elliptic surfaces. Zbl 1326.14017Katz, Nicholas M. 2 2015 Report on the irreducibility of \(L\)-functions. Zbl 1276.11147Katz, Nicholas M. 2 2012 Automorphic realization of residual Galois representations. Zbl 1257.11051Guralnick, Robert; Harris, Michael; Katz, Nicholas M. 2 2010 Perversity and exponential sums. II: Estimates for and inequalities among \(A\)-numbers. Zbl 0837.14017Katz, Nicholas M. 2 1994 The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume I. Zbl 0717.00008Cartier, P. (ed.); Illusie, L. (ed.); Katz, N. M. (ed.); Laumon, G. (ed.); Manin, Y. (ed.); Ribet, K. A. (ed.) 2 1990 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 Free actions of finite groups on varieties. II. Zbl 0551.14019Browder, William; Katz, Nicholas M. 2 1982 Le niveau de la cohomologie des intersections complètes. Appendice par P. Deligne. Zbl 0288.14001Katz, N. 2 1973 Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\). Zbl 1446.11210Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 1 2020 Local systems and finite unitary and symplectic groups. Zbl 1425.14009Katz, Nicholas M.; Tiep, Pham Huu 1 2019 Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\). Zbl 1446.11210Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu 1 2020 Rigid local systems and alternating groups. Zbl 1454.11217Guralnick, Robert; Katz, Nicholas; Tiep, Pham Huu 4 2019 A rigid local system with monodromy group \(2.J_{2}\). Zbl 07067789Katz, Nicholas M.; Rojas-León, Antonio 3 2019 Rigid local systems and finite symplectic groups. Zbl 1459.11225Katz, Nicholas M.; Tiep, Pham Huu 2 2019 Local systems and finite unitary and symplectic groups. Zbl 1425.14009Katz, Nicholas M.; Tiep, Pham Huu 1 2019 Rigid local systems on \(\mathbb{A}^{1}\) with finite monodromy. Zbl 1456.11232Katz, Nicholas M. 7 2018 Witt vectors and a question of Rudnick and Waxman. Zbl 1405.13040Katz, Nicholas M. 2 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 1338.01022Artin, Michael (ed.); Jackson, Allyn (ed.); Mumford, David (ed.); Tate, John (ed.); 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 1416.11082Katz, Nicholas M. 3 2015 Elliptic convolution, \(G_2\), and elliptic surfaces. Zbl 1326.14017Katz, Nicholas M. 2 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 Entin, Keating, and Rudnick. Zbl 1346.13045Katz, Nicholas M. 1 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 Keating and Rudnick. Zbl 1328.13028Katz, Nicholas M. 9 2013 On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor. Zbl 1358.11127Katz, Nicholas M. 6 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. 10 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. 3 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 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 From Clausen to Carlitz: low-dimensional spin groups and identities among character sums. Zbl 1234.11103Katz, Nicholas M. 1 2009 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. 19 2005 Cohomological divisibility and point count divisibility. Zbl 1076.14028Esnault, Hélène; Katz, Nicholas M. 1 2005 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 Inequalities related to Lefschetz pencils and integrals of Chern classes. Zbl 1092.14016Katz, Nicholas M.; Pandharipande, Rahul 1 2004 Geometric aspects of Dwork theory. Vol. I, II. Zbl 1047.14001Adolphson, Alan (ed.); Baldassarri, Francesco (ed.); Berthelot, Pierre (ed.); Katz, Nicholas (ed.); Loeser, François (ed.) 1 2004 A semicontinuity result for monodromy under degeneration. Zbl 1070.14024Katz, Nicholas M. 5 2003 Estimates for nonsingular multiplicative character sums. Zbl 1028.11075Katz, Nicholas M. 14 2002 Twisted \(L\)-functions and monodromy. Zbl 1029.14005Katz, Nicholas M. 11 2002 Sums of Betti numbers in arbitrary characteristic. Zbl 1068.14501Katz, Nicholas M. 20 2001 A general stratification theorem for exponential sums, and applications. Zbl 0986.11054Fouvry, E.; Katz, N. 17 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. 9 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 205 1999 Zeroes of zeta functions and symmetry. Zbl 0921.11047Katz, Nicholas M.; Sarnak, Peter 119 1999 Estimates for “singular” exponential sums. Zbl 0991.11064Katz, Nicholas M. 16 1999 Bernard Dwork (1923–1998). Zbl 1177.01050Katz, Nicholas M.; Tate, John 1 1999 Rigid local systems. Zbl 0864.14013Katz, Nicholas M. 86 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. 22 1993 Affine cohomological transforms, perversity, and monodromy. Appendix (d’après Deligne). Zbl 0815.14011Katz, Nicholas M. 8 1993 Exponential sums and differential equations. Zbl 0731.14008Katz, Nicholas M. 112 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 0717.00008Cartier, P. (ed.); Illusie, L. (ed.); Katz, N. M. (ed.); Laumon, G. (ed.); Manin, Y. (ed.); Ribet, K. A. (ed.) 2 1990 The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck. Volume II. Zbl 0717.00009Cartier, P. (ed.); Illusie, L. (ed.); Katz, N. M. (ed.); Laumon, G. (ed.); Manin, Y. (ed.); Ribet, K. A. (ed.) 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 21 1989 An estimate for character sums. Zbl 0672.10026Katz, Nicholas M. 19 1989 Perversity and exponential sums. Zbl 0755.14008Katz, Nicholas M. 8 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. 144 1988 Travaux de Laumon. (Works of Laumon). Zbl 0698.14014Katz, Nicholas M. 9 1988 On the calculation of some differential Galois groups. Zbl 0609.12025Katz, Nicholas M. 44 1987 On the monodromy groups attached to certain families of exponential sums. Zbl 0643.12004Katz, Nicholas M. 24 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. 39 1986 Arithmetic moduli of elliptic curves. Zbl 0576.14026Katz, Nicholas M.; Mazur, Barry 236 1985 Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.). Zbl 0603.14015Katz, Nicholas M.; Laumon, Gérard 47 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. 5 1985 Wild ramification and some problems of ”independence of \(\ell ''\). Zbl 0568.14012Katz, Nicholas M. 3 1983 On the ubiquity of ”pathology” in products. Zbl 0574.14021Katz, Nicholas M. 1 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. 4 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. 42 1981 Serre-Tate local moduli. Zbl 0477.14007Katz, N. 41 1981 Finiteness theorems in geometric classfield theory. (With an appendix by Kenneth A. Ribet). Zbl 0495.14011Katz, Nicholas M.; Lang, Serge 34 1981 Divisibilities, congruences, and Cartier duality. Zbl 0559.14032Katz, Nicholas M. 13 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 Monodromy of families of curves: Applications of some results of Davenport-Lewis. Zbl 0475.14025Katz, Nicholas M. 1 1981 Sommes exponentielles. Cours à Orsay, automne 1979. Redige par Gerard Laumon, preface par Luc Illusie. Zbl 0469.12007Katz, Nicholas M. 20 1980 The work of Pierre Deligne. Zbl 0441.14001Katz, N. M. 1 1980 p-adic L-functions, Serre-Tate local moduli, and ratios of solutions of differential equations. Zbl 0439.12010Katz, Nicholas M. 1 1980 Slope filtration of F-crystals. Zbl 0426.14007Katz, Nicholas M. 65 1979 \(p\)-adic \(L\)-functions for CM fields. Zbl 0417.12003Katz, Nicholas M. 92 1978 The Eisenstein measure and p-adic interpolation. Zbl 0375.12022Katz, Nicholas M. 26 1977 Formal groups and p-adic interpolation. Zbl 0351.14024Katz, Nicholas M. 10 1977 ...and 24 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,713 Authors 41 Katz, Nicholas Michael 30 Shparlinski, Igor E. 18 Hida, Haruzo 18 Sperber, Steven I. 16 Miller, Steven J. 16 Wan, Daqing 15 Kowalski, Emmanuel 14 Michel, Philippe Gabriel 13 Adolphson, Alan 13 Fouvry, Etienne 12 Esnault, Hélène 12 Gross, Benedict Hyman 12 Harris, Michael Howard 12 Panchishkin, Alexei A. 12 Tiep Pham Huu 11 Rojas-León, Antonio 11 Zaharescu, Alexandru 10 Keating, Jonathan P. 10 van der Put, Marius 9 André, Yves 9 Buium, Alexandru 9 Katz, Daniel J. 9 Poonen, Bjorn 8 Achter, Jeffrey D. 8 Barman, Rupam 8 Chen, Imin 8 Coleman, Robert Frederick 8 Crew, Richard M. 8 Dettweiler, Michael 8 Evans, Ronald J. 8 Mazur, Barry 8 Reiter, Stefan 8 Tilouine, Jacques 8 Ulmer, Douglas L. 8 Xi, Ping 7 Burungale, Ashay A. 7 Chiarellotto, Bruno 7 Darmon, Henri René 7 de Shalit, Ehud 7 Dwork, Bernard Morris 7 Fu, Lei 7 Goren, Eyal Z. 7 Guerzhoy, Pavel I. 7 Guralnick, Robert Michael 7 Pries, Rachel J. 7 Roques, Julien 7 Rudnick, Zeév 7 Sarnak, Peter Clive 7 Sawin, William F. 7 Snaith, Nina Claire 7 Voloch, José Felipe 6 Andrade, Julio Cesar 6 Berthelot, Pierre 6 Biswas, Indranil 6 Böckle, Gebhard 6 Cao, Wei 6 Castro, Francis Noel 6 Etesse, Jean-Yves 6 Goss, David 6 Haraoka, Yoshishige 6 Illusie, Luc 6 Langevin, Philippe 6 Pink, Richard 6 Rubinstein, Michael O. 6 Suh, Junecue 6 Zhu, Hui June 5 Andreatta, Fabrizio 5 Baldassarri, Francesco 5 Chandee, Vorrapan 5 Cohen, Stephen D. 5 Cullinan, John 5 David, Chantal 5 Eischen, Ellen Elizabeth 5 Forrester, Peter J. 5 Gillard, Roland 5 Gros, Michel 5 Hall, Chris 5 Hoshi, Yuichiro 5 Howe, Everett W. 5 Hsieh, Ming-Lun 5 Kerz, Moritz C. 5 Kobayashi, Shinichi 5 Lachaud, Gilles 5 Lan, Kai-Wen 5 Lauder, Alan G. B. 5 Milne, James Stuart 5 Movasati, Hossein 5 Ogus, Arthur 5 Oort, Frans 5 Roditty-Gershon, Edva 5 Rotger, Victor 5 Rubin, Karl Cooper 5 Rubio, Ivelisse M. 5 Sheng, Mao 5 Taylor, Richard Lawrence 5 Tsuzuki, Nobuo 5 Xiao, Liang 5 Xiong, Maosheng 5 Zarkhin, Yuriĭ Gennad’evich 5 Zhang, Wenpeng ...and 1,613 more Authors all top 5 Cited in 212 Serials 177 Journal of Number Theory 102 Inventiones Mathematicae 87 Duke Mathematical Journal 81 Compositio Mathematica 66 Annales de l’Institut Fourier 64 Transactions of the American Mathematical Society 61 Mathematische Annalen 55 Finite Fields and their Applications 51 Advances in Mathematics 50 Journal of Algebra 42 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 41 Proceedings of the American Mathematical Society 41 International Journal of Number Theory 34 Mathematische Zeitschrift 34 Journal de Théorie des Nombres de Bordeaux 30 Israel Journal of Mathematics 26 Annals of Mathematics. 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Mathematics 4 Forum of Mathematics, Pi 4 Annales Mathématiques du Québec 3 Bulletin of the Australian Mathematical Society 3 Discrete Applied Mathematics 3 The Annals of Probability 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Canadian Journal of Mathematics 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 112 more Serials all top 5 Cited in 51 Fields 1,203 Number theory (11-XX) 996 Algebraic geometry (14-XX) 113 Field theory and polynomials (12-XX) 99 Group theory and generalizations (20-XX) 99 Several complex variables and analytic spaces (32-XX) 86 Special functions (33-XX) 85 Ordinary differential equations (34-XX) 73 Commutative algebra (13-XX) 49 Combinatorics (05-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 46 Topological groups, Lie groups (22-XX) 42 Probability theory and stochastic processes (60-XX) 40 Algebraic topology (55-XX) 36 Quantum theory (81-XX) 31 \(K\)-theory (19-XX) 26 Category theory; homological algebra (18-XX) 25 Associative rings and algebras (16-XX) 24 Information and communication theory, circuits (94-XX) 23 Dynamical systems and ergodic theory (37-XX) 22 Global analysis, analysis on manifolds (58-XX) 22 Computer science (68-XX) 20 Differential geometry (53-XX) 15 Nonassociative rings and algebras (17-XX) 14 Partial differential equations (35-XX) 14 Statistical mechanics, structure of matter (82-XX) 11 Manifolds and cell complexes (57-XX) 8 Difference and functional equations (39-XX) 8 Convex and discrete geometry (52-XX) 7 General and overarching topics; collections (00-XX) 6 Functions of a complex variable (30-XX) 6 Approximations and expansions (41-XX) 6 Abstract harmonic analysis (43-XX) 6 Functional analysis (46-XX) 6 Operator theory (47-XX) 5 History and biography (01-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Geometry (51-XX) 4 Mathematical logic and foundations (03-XX) 4 Numerical analysis (65-XX) 3 Measure and integration (28-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistics (62-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Integral equations (45-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-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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