TY - BOOK
T1 - Convolution and equidistribution
T2 - Sato-Tate theorems for finite-field Mellin transforms
AU - Katz, Nicholas M.
N1 - Publisher Copyright:
© 2012 by Princeton University Press. All Rights Reserved.
PY - 2012/1/24
Y1 - 2012/1/24
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84924292956&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84924292956&partnerID=8YFLogxK
M3 - Book
AN - SCOPUS:84924292956
SN - 9780691153308
BT - Convolution and equidistribution
PB - Princeton University Press
ER -