(DOWNLOAD) "Convolution and Equidistribution" by Nicholas M. Katz # eBook PDF Kindle ePub Free
eBook details
- Title: Convolution and Equidistribution
- Author : Nicholas M. Katz
- Release Date : January 24, 2012
- Genre: Mathematics,Books,Science & Nature,Algebra,Statistics,Geometry,Professional & Technical,
- Pages : * pages
- Size : 6762 KB
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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