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

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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.

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Additional ISBNs
9780691153315

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