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.
| Autorius: | Nicholas M. Katz |
| Leidėjas: | Princeton University Press |
| Išleidimo metai: | 2012 |
| Knygos puslapių skaičius: | 212 |
| ISBN-10: | 0691153310 |
| ISBN-13: | 9780691153315 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Number theory |
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