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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)
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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Hardback)

£158.00
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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.

Science & MathematicsMathematicsCalculus & mathematical analysisCalculusScience & MathematicsMathematicsCalculus & mathematical analysisCalculus of variationsScience & MathematicsMathematicsGeometryAlgebraic geometryScience & MathematicsMathematicsNumber theory Publisher: Princeton University Press Publication Date: 24/01/2012 ISBN-13: 9780691153308  Details: Type: Hardback Format: Books
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Nicholas M. Katz is professor of mathematics at Princeton University. He is the author or coauthor of six previous titles in the Annals of Mathematics Studies: "Arithmetic Moduli of Elliptic Curves "(with Barry Mazur); "Gauss Sums, Kloosterman Sums, and Monodromy Groups"; "Exponential Sums and Differential Equations"; "Rigid Local Systems"; "Twisted L-Functions and Monodromy;" and "Moments, Monodromy, and Perversity."

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