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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (Am-180) (Annals of Mathematics Studies)
Nicholas M. Katz (Author)
·
Princeton University Press
· Paperback
Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (Am-180) (Annals of Mathematics Studies) - Nicholas M. Katz
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Synopsis "Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (Am-180) (Annals of Mathematics Studies)"
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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The book is written in English.
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