Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms
Hardcover
Paperback
- Sale Price:
- £26.40
- Price:
-
$104.00/
£88.00 - ISBN:
- Published:
- Jan 24, 2012
- Copyright:
- 2012
- Pages:
- 208
- Size:
- 6 x 9.25 in.
- Main_subject:
- Mathematics
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ebook
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.