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Convolution and Equidistribution

- Sato-Tate Theorems for Finite-Field Mellin Transforms
Af: Nicholas M. Katz Engelsk Paperback

Convolution and Equidistribution

- Sato-Tate Theorems for Finite-Field Mellin Transforms
Af: Nicholas M. Katz Engelsk Paperback
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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.


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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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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Produktdetaljer
Sprog: Engelsk
Sider: 208
ISBN-13: 9780691153315
Indbinding: Paperback
Udgave:
ISBN-10: 0691153310
Kategori: Talteori
Udg. Dato: 24 jan 2012
Længde: 12mm
Bredde: 157mm
Højde: 233mm
Forlag: Princeton University Press
Oplagsdato: 24 jan 2012
Forfatter(e): Nicholas M. Katz
Forfatter(e) Nicholas M. Katz

Kategori Talteori

ISBN-13 9780691153315

Sprog Engelsk

Indbinding Paperback

Sider 208

Udgave

Længde 12mm

Bredde 157mm

Højde 233mm

Udg. Dato 24 jan 2012

Oplagsdato 24 jan 2012

Forlag Princeton University Press