Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms
- Nicholas M. Katz.
- Princeton [N.J.] : Princeton University Press, 2012.
- Physical description
- vi, 203 p. ; 24 cm.
- Annals of mathematics studies no. 180.
Science Library (Li and Ma)
|Shelved by Series title NO.180||Unknown|
- Katz, Nicholas M., 1943-
- Includes bibliographical references (p. 193-195) and index.
- Publisher's Summary
- "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.
(source: Nielsen Book Data)9780691153315 20160607
- Publication date
- Annals of mathematics studies ; no. 180
- 9780691153308 (hardcover : alk. paper)
- 0691153302 (hardcover : alk. paper)
- 9780691153315 (pbk. : alk. paper)
- 0691153310 (pbk. : alk. paper)
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