Convolution and Equidistribution

English

Series: Annals of Mathematics Studies

ISBN: 1400842700

EAN: 9781400842704

Category: Mathematics / General

Publisher: Princeton University Press

Release Date: 01/23/2012

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.

Excerpt: Unknown Property Excerpt

Convolution and Equidistribution

Illustrated: No

Format: eBook - PDF

Pages: 212