**Book Description:**

*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.

**eISBN:**978-1-4008-4270-4

**Subjects:**Mathematics, Statistics