Nicholas Katz - Profile on Academia.edu (original) (raw)

Papers by Nicholas Katz

A note on Galois representations with big image

L’Enseignement Mathématique

Tunisian Journal of Mathematics

Contents 1. Introduction 1 2. The local systems in general 2 3. The candidate local systems for A... more Contents 1. Introduction 1 2. The local systems in general 2 3. The candidate local systems for Alt(2q) 4 4. Basic facts about H n 5 5. basic facts about H 2q−1 6 6. Basic facts about the group G geom for F (k, 2q − 1, ψ) 7 7. The third moment of F (k, 2q − 1, ψ) and of G(k, 2q − 1, ψ) 8 8. Exact determination of G arith 11 9. Identifying the group 12 References 25

On a Question of Zannier

Experimental Mathematics

Moscow Mathematical Journal

Annales scientifiques de l'École normale supérieure

International Mathematics Research Notices

Witt vectors and a question of Keating and Rudnick" [12]. We prove equidistribution results for t... more Witt vectors and a question of Keating and Rudnick" [12]. We prove equidistribution results for the L-functions attached to "super-even" characters of the group of truncated "big" Witt vectors, and for the L-functions attached to the twists of these characters by the quadratic character. We work over a finite field k = F q of characteristic p inside a fixed algebraic closure k, and fix an odd integer n ≥ 3. We form the k-algebra Following Rudnick and Waxman, we say that a character If is nontrivial and super-even, one defines its L-function L(A 1 /k, , T), a priori a formal power series, by L(A 1 /k, , T) := (1 -T) -1 P monic irreducible P(0) =0 (1 -(P)T deg P ) -1 ,

Annales scientifiques de l'École normale supérieure

Internal reconstruction of unit-root F-crystals via expansioncoefficients. With an appendix by Lu... more Internal reconstruction of unit-root F-crystals via expansioncoefficients. With an appendix by Luc Illusie Annales scientifiques de l'É.N.S. 4 e série, tome 18, n o 2 (1985), p. 245-285. <http://www.numdam.org/item?id=ASENS_1985_4_18_2_245_0> © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1985, tous droits réservés. L'accès aux archives de la revue « Annales scientifiques de l'É.N.S. » (http://www. elsevier.com/locate/ansens), implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Journal of Mathematics of Kyoto University

Bulletin de la Société mathématique de France, 1982

Bulletin de la S. M. F., tome 110 (1982), p. 347-348 <http © Bulletin de la S. M. F., 1982, tous ... more Bulletin de la S. M. F., tome 110 (1982), p. 347-348 <http © Bulletin de la S. M. F., 1982, tous droits réservés. L'accès aux archives de la revue « Bulletin de la S. M. F. » () implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

Bulletin de la Société mathématique de France, 1982

http://www.numdam.org/item?id=BSMF\_1982\_\_110\_\_203\_0 © Bulletin de la S. M. F., 1982, tous droit... more <http://www.numdam.org/item?id=BSMF_1982__110__203_0> © Bulletin de la S. M. F., 1982, tous droits réservés. L'accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html), implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Colloquium Publications, 1998

The main topic of this book is the deep relation between the spacings between zeros of zeta and L... more The main topic of this book is the deep relation between the spacings between zeros of zeta and L-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and L-functions over finite fields. The book draws on, and gives accessible accounts of, many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Well Conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants. It will be useful and interesting to researchers and graduate students working in any of these areas.

Groupes de Monodromie en Géométrie Algébrique

Lecture Notes in Mathematics, 1972

Slope filtration of F-crystals

Asterisque Societe Mathematique De France, 1979

Monodromy and the Tate Conjecture: Picard numbers and Mordell-Weil ranks in families

Israel Journal of Mathematics, 2000

Introduction We use results of Deligne on …-adic monodromy and equidistribution, combined with el... more Introduction We use results of Deligne on …-adic monodromy and equidistribution, combined with elementary facts about the eigenvalues of elements in the orthogonal group, to give upper bounds for the average &quot;middle Picard number&quot; in various equicharacteristic families of ...

Bernard Dwork (1923–1998)

Notices of the American Mathematical Society, 1999

[

Corrigendum to "G2 and hypergeometric sheaves" [Finite Fields Appl

Ffa, 2008

On a certain class of exponential sums

J Reine Angew Math, 1987

The Grothendieck Festschrift : a collection of articles written in honor of the 60th birthday of Alexander Grothendieck

International Mathematics Research Notices, 2014

This is Part II of the paper "A question of Keating and Rudnick about primitive Dirichlet charact... more This is Part II of the paper "A question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor" [Ka-QKRPD]. Here we prove two independence results for tuples of character sums, either formed with a variable character and its powers, or formed with two characters and their product.

A note on Galois representations with big image

L’Enseignement Mathématique

Tunisian Journal of Mathematics

Contents 1. Introduction 1 2. The local systems in general 2 3. The candidate local systems for A... more Contents 1. Introduction 1 2. The local systems in general 2 3. The candidate local systems for Alt(2q) 4 4. Basic facts about H n 5 5. basic facts about H 2q−1 6 6. Basic facts about the group G geom for F (k, 2q − 1, ψ) 7 7. The third moment of F (k, 2q − 1, ψ) and of G(k, 2q − 1, ψ) 8 8. Exact determination of G arith 11 9. Identifying the group 12 References 25

On a Question of Zannier

Experimental Mathematics

Moscow Mathematical Journal

Annales scientifiques de l'École normale supérieure

International Mathematics Research Notices

Witt vectors and a question of Keating and Rudnick" [12]. We prove equidistribution results for t... more Witt vectors and a question of Keating and Rudnick" [12]. We prove equidistribution results for the L-functions attached to "super-even" characters of the group of truncated "big" Witt vectors, and for the L-functions attached to the twists of these characters by the quadratic character. We work over a finite field k = F q of characteristic p inside a fixed algebraic closure k, and fix an odd integer n ≥ 3. We form the k-algebra Following Rudnick and Waxman, we say that a character If is nontrivial and super-even, one defines its L-function L(A 1 /k, , T), a priori a formal power series, by L(A 1 /k, , T) := (1 -T) -1 P monic irreducible P(0) =0 (1 -(P)T deg P ) -1 ,

Annales scientifiques de l'École normale supérieure

Internal reconstruction of unit-root F-crystals via expansioncoefficients. With an appendix by Lu... more Internal reconstruction of unit-root F-crystals via expansioncoefficients. With an appendix by Luc Illusie Annales scientifiques de l'É.N.S. 4 e série, tome 18, n o 2 (1985), p. 245-285. <http://www.numdam.org/item?id=ASENS_1985_4_18_2_245_0> © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1985, tous droits réservés. L'accès aux archives de la revue « Annales scientifiques de l'É.N.S. » (http://www. elsevier.com/locate/ansens), implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Journal of Mathematics of Kyoto University

Bulletin de la Société mathématique de France, 1982

Bulletin de la S. M. F., tome 110 (1982), p. 347-348 <http © Bulletin de la S. M. F., 1982, tous ... more Bulletin de la S. M. F., tome 110 (1982), p. 347-348 <http © Bulletin de la S. M. F., 1982, tous droits réservés. L'accès aux archives de la revue « Bulletin de la S. M. F. » () implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

Bulletin de la Société mathématique de France, 1982

http://www.numdam.org/item?id=BSMF\_1982\_\_110\_\_203\_0 © Bulletin de la S. M. F., 1982, tous droit... more <http://www.numdam.org/item?id=BSMF_1982__110__203_0> © Bulletin de la S. M. F., 1982, tous droits réservés. L'accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html), implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Colloquium Publications, 1998

The main topic of this book is the deep relation between the spacings between zeros of zeta and L... more The main topic of this book is the deep relation between the spacings between zeros of zeta and L-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and L-functions over finite fields. The book draws on, and gives accessible accounts of, many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Well Conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants. It will be useful and interesting to researchers and graduate students working in any of these areas.

Groupes de Monodromie en Géométrie Algébrique

Lecture Notes in Mathematics, 1972

Slope filtration of F-crystals

Asterisque Societe Mathematique De France, 1979

Monodromy and the Tate Conjecture: Picard numbers and Mordell-Weil ranks in families

Israel Journal of Mathematics, 2000

Introduction We use results of Deligne on …-adic monodromy and equidistribution, combined with el... more Introduction We use results of Deligne on …-adic monodromy and equidistribution, combined with elementary facts about the eigenvalues of elements in the orthogonal group, to give upper bounds for the average &quot;middle Picard number&quot; in various equicharacteristic families of ...

Bernard Dwork (1923–1998)

Notices of the American Mathematical Society, 1999

[

Corrigendum to "G2 and hypergeometric sheaves" [Finite Fields Appl

Ffa, 2008

On a certain class of exponential sums

J Reine Angew Math, 1987

The Grothendieck Festschrift : a collection of articles written in honor of the 60th birthday of Alexander Grothendieck

International Mathematics Research Notices, 2014

This is Part II of the paper "A question of Keating and Rudnick about primitive Dirichlet charact... more This is Part II of the paper "A question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor" [Ka-QKRPD]. Here we prove two independence results for tuples of character sums, either formed with a variable character and its powers, or formed with two characters and their product.