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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms
Paperback
Series: Annals of Mathematics Studies, Book 180
CalculusGeneral MathematicsProbability & Statistics
ISBN13: 9780691153315
Publisher: Princeton Univ Pr
Published: Jan 24 2012
Pages: 208
Weight: 0.70
Height: 0.60 Width: 6.10 Depth: 9.10
Language: English
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.1 different editions
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