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Convolution and Equidistribution: SatoTate Theorems for FiniteField Mellin Transforms (Am180) (Annals of Mathematics Studies)by Nicholas M. Katz
Synopses & ReviewsPublisher Comments:Convolution and Equidistribution explores an important aspect of number theorythe theory of exponential sums over finite fields and their Mellin transformsfrom 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 finitefield 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 algebrogeometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and grouptheoretic 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. Synopsis:Convolution and Equidistribution explores an important aspect of number theorythe theory of exponential sums over finite fields and their Mellin transformsfrom 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 finitefield 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 algebrogeometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and grouptheoretic 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. Synopsis:Convolution and Equidistribution explores an important aspect of number theorythe theory of exponential sums over finite fields and their Mellin transformsfrom 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 finitefield 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 algebrogeometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and grouptheoretic 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. About the AuthorNicholas 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 LFunctions and Monodromy;" and "Moments, Monodromy, and Perversity."
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