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

Nicholas M. Katz

ISBN 10: 0691153310 / ISBN 13: 9780691153315

Edité par Princeton University Press, 2012

A propos de cet article

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9780691153315

Détails bibliographiques

• Titre: Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms
• Éditeur: Princeton University Press
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 0691153310
• ISBN à 13 chiffres: 9780691153315
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 234 L x 156 H x 12 P (en millimètres) 234 millimètres de largeur par 156 millimètres de hauteur par 12 millimètres de profondeur
• Poids: 330 grammes

A propos de ce titre

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.

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.