Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms - Couverture souple

Katz, Nicholas M.

Couverture souple

ISBN 10 : 0691153310 ISBN 13 : 9780691153315

Editeur : Princeton University Press, 2012

Synopsis

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.

A propos du livre

À propos de l'auteur

Nicholas M. Katz is professor of mathematics at Princeton University. He is the author or coauthor of six previous titles in the Annals of Mathematics Studies: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; Rigid Local Systems; Twisted L-Functions and Monodromy; and Moments, Monodromy, and Perversity.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 0691153310
• ISBN 13: 9780691153315
• Reliure: Broché
• Nombre de pages: 208
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible