Convolution and equidistribution : sato-tate theorems for finite-field mellin transforms
Enregistré dans:
| Auteur principal: | |
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| Support: | E-Book |
| Langue: | Anglais |
| Publié: |
Princeton ; N.J :
Princeton University Press,
2012.
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| Collection: | Annals of Mathematics Studies ;
180 |
| Sujets: | |
| Autres localisations: | Voir dans le Sudoc |
| Résumé: | 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." |
| Accès en ligne: | Accès à l'E-book |
| Lien: | Collection principale:
Annals of Mathematics Studies |
| Résumé: | 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 |
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| Description: | La pagination de l'édition imprimée correspondante est de : 208 p. |
| Support: | Nécessite un navigateur et un lecteur de fichier PDF. |
| ISBN: | 9781400842704 |
| Accès: | L'accès complet à la ressource est réservé aux usagers des établissements qui en ont fait l'acquisition |