Convolution and equidistribution : sato-tate theorems for finite-field mellin transforms

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Detaylı Bibliyografya
Yazar: Katz, Nicholas M. (1943-....). (Yazar)
Materyal Türü: E-Book
Dil: Anglais
Baskı/Yayın Bilgisi: Princeton ; N.J : Princeton University Press, 2012.
Seri Bilgileri: Annals of Mathematics Studies ; 180
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Özet: Biographical note: KatzNicholas M.: 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."
Online Erişim: Accès à l'E-book
İlgili Kayıtlar: Ana seri: Annals of Mathematics Studies
Diğer Bilgiler
Özet:Biographical note: KatzNicholas M.: 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."
Main description: 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
Diğer Bilgileri:La pagination de l'édition imprimée correspondante est de : 208 p.
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ISBN:9781400842704
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