Nicholas M. Katz: Convolution and Equidistribution
Convolution and Equidistribution
Buch
- Sato-Tate Theorems for Finite-Field Mellin Transforms
- Princeton University Press, 01/2012
- Einband: Kartoniert / Broschiert, Paperback
- Sprache: Englisch
- ISBN-13: 9780691153315
- Bestellnummer: 1923279
- Umfang: 212 Seiten
- Copyright-Jahr: 2012
- Gewicht: 330 g
- Maße: 234 x 156 mm
- Stärke: 11 mm
- Erscheinungstermin: 24.1.2012
Achtung: Artikel ist nicht in deutscher Sprache!
Weitere Ausgaben von Convolution and Equidistribution
Beschreibung
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.Klappentext
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.