Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms
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| Title: | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms |
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| 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. |
| Authors: | Nicholas M. Katz |
| Resource Type: | eBook. |
| Subjects: | Convolutions (Mathematics), Mellin transform, Sequences (Mathematics) |
| Categories: | MATHEMATICS / Number Theory, MATHEMATICS / Finite Mathematics, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Group Theory, MATHEMATICS / Probability & Statistics / General |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | 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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| ISBN: | 9780691153315 9780691153308 9781400842704 |
