Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

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. Additional ISBNs 9780691153315Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) is written by Nicholas M. Katz and published by Princeton University Press. ISBNs for Convolution and Equidistribution are 9781400842704, 1400842700 and the print ISBNs are 9780691153308, 0691153302. Additional ISBNs include 9780691153315.