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 The Right Wrong Man by Nicholas M. Katz
Cover of the book Marx's Inferno by Nicholas M. Katz
Cover of the book Self-Regularity by Nicholas M. Katz
Cover of the book Knowing the Adversary by Nicholas M. Katz
Cover of the book Thrive by Nicholas M. Katz
Cover of the book The Reasons of Love by Nicholas M. Katz
Cover of the book The Complexity of Cooperation by Nicholas M. Katz
Cover of the book Beyond the Invisible Hand by Nicholas M. Katz
Cover of the book Giacomo Puccini and His World by Nicholas M. Katz
Cover of the book Gifted Tongues by Nicholas M. Katz
Cover of the book Emblems of Pluralism by Nicholas M. Katz
Cover of the book How to Do Things with Books in Victorian Britain by Nicholas M. Katz
Cover of the book Beyond Our Means by Nicholas M. Katz
Cover of the book The Meaning of the Library by Nicholas M. Katz
Cover of the book Picture Titles 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