Convolution and Equidistribution

Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Nonfiction, Science & Nature, Mathematics, Number Theory, Statistics
Cover of the book Convolution and Equidistribution by Nicholas M. Katz, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Nicholas M. Katz ISBN: 9781400842704
Publisher: Princeton University Press Publication: January 24, 2012
Imprint: Princeton University Press Language: English
Author: Nicholas M. Katz
ISBN: 9781400842704
Publisher: Princeton University Press
Publication: January 24, 2012
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book Shakespeare by Nicholas M. Katz
Cover of the book Collected Works of C.G. Jung, Volume 16 by Nicholas M. Katz
Cover of the book Money Talks by Nicholas M. Katz
Cover of the book Fault Lines: How Hidden Fractures Still Threaten the World Economy by Nicholas M. Katz
Cover of the book The Tar Baby by Nicholas M. Katz
Cover of the book How Ancient Europeans Saw the World by Nicholas M. Katz
Cover of the book Birds of Peru by Nicholas M. Katz
Cover of the book The Birth of Politics by Nicholas M. Katz
Cover of the book The New Worlds of Thomas Robert Malthus by Nicholas M. Katz
Cover of the book The Global Commonwealth of Citizens by Nicholas M. Katz
Cover of the book Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179) by Nicholas M. Katz
Cover of the book The Way We Argue Now by Nicholas M. Katz
Cover of the book Liberty and Coercion by Nicholas M. Katz
Cover of the book The Emergence of Organizations and Markets by Nicholas M. Katz
Cover of the book Classical Mathematical Logic by Nicholas M. Katz
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy