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Book 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.

Book details

Book category Books in English Mathematics & science Mathematics Number theory

• Full title: Convolution and Equidistribution
• Author: Katz
• Language: English
• Binding: Paperback
• Number of pages: 208
• EAN: 9780691153315
• ISBN: 0691153310
• ID: 04460051
• Publisher: Princeton University Press
• Weight: 314 g
• Dimensions: 233 × 157 × 12 mm
• Date of publishing: 24. January 2012

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