Bibliography of Nicholas M. Katz

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C.V. of Nicholas M. Katz

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Photo from 60'th Birthday Conference

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Photo from 60'th Birthday Conference (high resolution version)

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V-Strom DL650 suspension adjustment

fans of MONODROMY.COM can find most of it at its new home

Nicholas M. Katz PDF and DVI files available for download

Some older work can be found HERE (listed alphabetically by title) recent work is below (most recent first)

(joint with Pham Huu Tiep)Moments, exponential sums, and monodromy groups

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(joint with Pham Huu Tiep) Condition (S+) in ranks 4,8, and 9

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(joint with Pham Huu Tiep)Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups

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Some open questions about curves and abelian varieties over finite fields

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Erratum to "Nilpotent Connections and the Monodromy Theorem"

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(joint with Antonio Rojas-Leon and Pham Huu Tiep)Rigid Local Systems and Sporadic Simple Groups

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(joint with Levent Alpoge,Gabriel Navarro, E.A. O'Brien, and Pham Huu Tiep) Local Systems and Suzuki Groups

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Exponential Sums and Finite Groups(slides of talk at Luc Illusie 81 conference)

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(joint with Pham Huu Tiep)Hypergeometric Sheaves and Finite Symplectic and Unitary Groups

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(joint with Pham Huu Tiep) Exponential sums and total Weil representations of finite symplectic and unitary groups

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(revised version)pdf file(698 KB)

(joint with Pham Huu Tiep)MONODROMY GROUPS OF KLOOSTERMAN AND HYPERGEOMETRIC SHEAVES

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(joint with Pham Huu Tiep)Corrections to MONODROMY GROUPS OF KLOOSTERMAN AND HYPERGEOMETRIC SHEAVES

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(joint with Pham Huu Tiep) Rigid local systems and finite general linear groups

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(joint with Pham Huu Tiep)Moments of Weil representations of finite special unitary groups

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(joint with Antonio Rojas Leon and Pham Huu Tiep)A rigid local system with monodromy group the big Conway group 2.Co_1, and two others with monodromy group the Suzuki group 6.Suz

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(joint with Antonio Rojas Leon and Pham Huu Tiep) Rigid local systems with monodromy group the Conway group Co_2

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(joint with Antonio Rojas Leon and Pham Huu Tiep) Rigid local systems with monodromy group the Conway group Co_3

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(joint with Antonio Rojas Leon) A rigid local system with monodromy group 2.J_2

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How hard is it to be ordinary? (slides of talk at Loeser 60 conference)

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(joint with Pham Huu Tiep) Rigid local systems,moments, and finite unitary groups

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(joint with Pham Huu Tiep)Local systems and finite unitary and symplectic groups

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(joint with Pham Huu Tiep) Rigid local systems and finite symplectic groups

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(published version) pdf file (612 KB)

A note on galois representations with big image

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Rigid Local Systems and Alternating Groups (joint with Guralnick and Tiep), to appear in Tunisian Journal of Mathematics

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Exponential Sums, Ree Groups and Suzuki Groups:Conjectures

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published version pdf file(612 KB)

Corrigendum pdf file(92 KB)

Rigid local systems on \A^1 with finite monodromy (with an appendix by Pham Huu Tiep) to appear in Mathematika

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G_2 and some exceptional Witt vector identities

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Witt Vectors and a Question of Rudnick and Waxman

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A note on Random matrix integrals, moment identities, and Catalan numbers

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Searching for thin groups (slides of talk at Sarnak Birthday conference)

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On a question of Rudnick: do we have square root cancellation for error terms in moment calculations?

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ON TWO QUESTIONS OF ENTIN, KEATING, AND RUDNICK ON PRIMITIVE DIRICHLET CHARACTERS

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WITT VECTORS AND A QUESTION OF ENTIN,KEATING, AND RUDNICK

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Equidistribution questions arising from universal extensions(published version)

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Wieferich past and future

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A note on RH for curves and hypersurfaces over finite fields(typo's corrected Jan. 7, 2014)

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Sato-Tate in the higher dimensional case: elaboration of 9.5.4 in Serre's N_X(p) book

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On a question of Zannier

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published version pdf file(609K)

Elliptic convolution, G_2, and elliptic surfaces

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Simple Things We Don't Know

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On the graph attached to truncated big Witt vectors (Warning to the Reader, explaining relation to work of S.D.Cohen, added March 14, 2012)

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Witt vectors and a question of Keating and Rudnick(to appear in IMRN)

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On a question of Keating and Rudnick about primitive Dirichlet characters with squarefree conductor(new longer title: to appear in IMRN)

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Rigid Local Systems and a Problem of Wootters(typo's corrected Sept. 2012)

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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms(new title, now in book form, updated July 14, 2011)

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2,3,5, Legendre:\pm Trace ratios in families of elliptic curves (typo's corrected August 18, 2010)

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(joint with Guralnick and Harris) Automorphic realization of residual Galois representations

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Lang-Trotter revisited (published version)

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(joint with Bombieri)A Note on Lower Bounds for Frobenius Traces(revised Sept. 10, 2009)

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(joint with Dettweiler) Appendix: On Galois Representations with values in G_2 (appendix to a paper of Dettweiler and Reiter, to appear in Compositio)

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From Clausen to Carlitz: low-dimensional spin groups and identities among character sums

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Estimates for nonsingular mixed character sums (Thm. 3.1 improved Feb 19,2007, Appendix added and typo's corrected Feb. 24, more typo's fixed Aug 11, 2007)

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On a question of Bombieri and Bourgain(version of July 14, 2008; to appear in Forum Mathematicum)

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Another look at the Dwork family (revised Feb.4,2007; adds App. III,corrects more typo's)

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Manin Festschrift version (to appear) pdf file (354 KB)

Estimates for mixed character sums (to appear in GAFA)

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version to appear in GAFA pdf file (274 KB)

On a question of Browning and Heath-Brown

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version to appear in Analytic Number Theory: Essays in Honor or Klaus Roth

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Appendix: Lefschetz pencils with imposed subvarieties

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Report on the irreducibility of L-functions (to appear in Lang memorial volume)

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E-polynomials, zeta-equivalence, and polynomial-count varieties (appendix to a paper of Rodriguez-Villegas and Hausel)

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G_2 and hypergeometric sheaves (corrections to 10.1,10.2 added June 11,2008, correction to 9.1 added January 24, 2016)

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Corrections to "G_2 and hypergeometric sheaves" (as of January 42, 2016)

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On a question of Lillian Pierce

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Hooley parameters for families of exponential sums over finite fields

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Notes on G_2, determinants, and equidistribution (typo's corrected Dec. 9, 2003)

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(joint with Esnault) Cohomological divisibility and point count divisibility (corrected version of nov. 10, 2003)

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Corrected version of Chapter 5 of "Twisted L-Functions and Monodromy"

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Moments, Monodromy, and Perversity: a Diophantine Perspective

Space filling curves over finite fields (see corrections below)

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Corrections to "Space filling curves over finite fields"

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(joint with Pandharipande) Inequalities related to Lefschetz pencils and integrals of Chern classes

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(joint with Fouvry) A general stratification theorem for exponential sums, and applications

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Estimates for "nonsingular" multiplicative character sums

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A semicontinuity result for monodromy under degeneration

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Sato-Tate Equidistribution of Kurlberg-Rudnick Sums

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AWS2000 Lectures: L -functions and monodromy: four lectures on Weil II

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Larsen's Alternative, Moments, and the Monodromy of Lefschetz Pencils

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Sums of Betti numbers in arbitrary characteristic

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Frobenius-Schur indicator & the ubiquity of Brock-Granville Quadratic Excess

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Twisted L-Functions and Monodromy (whole book)

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Twisted L-Functions and Monodromy (introduction only)

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(joint with de Jong) Monodromy and the Tate Conjecture:Picard numbers and Mordell-Weil ranks in families

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Estimates for "singular" exponential sums

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(joint with Tate) Bernard Dwork (1923-1998)

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manuscript of Rigid Local Systems, with corrections

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Corrections to Rigid Local Systems

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manuscript of Exponential Sums and Differential Equations, with corrections

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Corrections to Exponential Sums and Differential Equations

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scan of Katz-Mazur (now searchable; downloads but does not open in Safari)

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Corrected version of 6.16.6 in Katz-Sarnak

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Katz-Sarnak the book, blurry but searchable

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Katz,Sommes Exponentielles, blurry but searchable

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Subject index to Katz-Sarnak

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Notation index to Katz-Sarnak

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Katz, Gauss Sums, Kloosterman Sums, and Monodromy

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djvu version djvu file (7.8 MB)

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