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

Nicholas M. Katz

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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.

Produktfakta

Språk Engelsk Engelsk Innbinding Heftet
Utgitt 2012 Forfatter Nicholas M. Katz
Forlag
University Press Group Ltd
ISBN 9780691153315
Antall sider 212 Dimensjoner 15,2cm x 22,9cm x 1,5cm
Vekt 314 gram Leverandør Bertram Trading Ltd
Emner og form Number theory