Convolution and Equidistribution
Sato-Tate Theorems for Finite-Field Mellin Transforms
(Sprache: Englisch)
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...
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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.
Bibliographische Angaben
- Autor: Nicholas M. Katz
- 2012, 208 Seiten, Maße: 23,7 cm, Kartoniert (TB), Englisch
- Verlag: Princeton University Press
- ISBN-10: 0691153310
- ISBN-13: 9780691153315
Sprache:
Englisch
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