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Convolution and Equidistribution

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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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