| Title:
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CONVOLUTION AND EQUIDISTRIBUTION
SATO-TATE THEOREMS FOR FINITE-FIELD MELLIN TRANSFORMS (AM-180) |
| By: |
Nicholas M. Katz |
| Format: |
Hardback |
| List price:
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£200.00 |
| Our price: |
£160.00 |
| Discount: |
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£40.00 |
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| ISBN 10: |
0691153302 |
| ISBN 13: |
9780691153308 |
| Availability: |
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| Stock: |
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| Publisher: |
PRINCETON UNIVERSITY PRESS |
| Pub. date: |
24 January, 2012 |
| Series: |
Annals of Mathematics Studies |
| Pages: |
208 |
| Description: |
Explores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
Princeton University Press |
| Returns: |
Returnable |
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