# Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) ebook

## by Nicholas M. Katz

Annals of mathematics studies ; no. 180. Bibliography, etc. Note: Includes bibliographical references (p. 193-195) and index. Download book Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms, Nicholas M. Katz.

Annals of mathematics studies ; no. Uniform Title: Annals of mathematics studies ; no. Rubrics: Mellin transform Convolutions (Mathematics) Sequences (Mathematics).

item 3 Convolution and Equidistribution: Sato-Tate The, Katz+ -Convolution and Equidistribution . Additional Product Features. Place of Publication. Annals of Mathematics Studies.

item 3 Convolution and Equidistribution: Sato-Tate The, Katz+ -Convolution and Equidistribution: Sato-Tate The, Katz+. item 4 Katz-Convolution and Equidistribution BOOK NEW -Katz-Convolution and Equidistribution BOOK NEW. £6. 0. 208. Author Biography. Nicholas M. Katz is professor of mathematics at Princeton University.

Publisher: Princeton University Press. Series: Annals of Mathematics Studies 180. Price: 7. Publication Date: 2012.

Katz, Nicholas M. Convolution and Equidistribution. Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180). Series:Annals of Mathematics Studies 180. See all formats and pricing. Please find details to our shipping fees here. RRP: Recommended Retail Price.

Convolution and Equidistribution. series Annals of Mathematics Studies

The basic question considered in the book is how the values of the Mellin.

The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric.

AM-116), Volume 116 (Annals of Mathematics Studies): Gauss Sums, Kloosterman Sums, and Monodromy Groups.

Exponential Sums and Differential Equations. AM-116), Volume 116 (Annals of Mathematics Studies): Gauss Sums, Kloosterman Sums, and Monodromy Groups.

Convolution and ores an important aspect of number theory-the theory of exponential sums over finite fields and their Mellin transforms-from a new, categorical point of view.

Katz studied, with Sarnak among others, the connection of the eigenvalue distribution of large random matrices of classical groups to the . Convolution and equidistribution: Sato-Tate theorems for finite-field Mellin transforms.

Katz studied, with Sarnak among others, the connection of the eigenvalue distribution of large random matrices of classical groups to the distribution of the distances of the zeros of various L and zeta functions in algebraic geometry. He also studied trigonometric sums (Gauss sums) with algebro-geometric methods. He introduced the Katz–Lang finiteness theorem. Convolution and equidistribution: Sato-Tate theorems for finite-field Mellin transforms With Barry Mazur: Arithmetic Moduli of elliptic curves.

The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters

The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods

*Convolution and Equidistribution* explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.

The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods.

By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.