CONVOLUTION AND EQUIDISTRIBUTION by Nicholas M. Katz ( 9780691153308 )

Item Details

Title:

CONVOLUTION AND EQUIDISTRIBUTION
SATO-TATE THEOREMS FOR FINITE-FIELD MELLIN TRANSFORMS (AM-180)

By:

Nicholas M. Katz

Format:

Hardback

List price:

£200.00

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£160.00

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20% off

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£40.00

ISBN 10:

0691153302

ISBN 13:

9780691153308

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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:

Imprint:

Princeton University Press

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Returnable

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