Ebook Info
- Published: 2012
- Number of pages: 224 pages
- Format: PDF
- File Size: 1.06 MB
- Authors: Nicholas M. Katz
Description
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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Free Download Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) in PDF format
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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) 2012 PDF Free Download
Download Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) PDF
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