Convolution and Equidistribution [electronic resource] : Sato-Tate Theorems for Finite-Field Mellin Transforms

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자료유형	단행본
서명/저자사항	Convolution and Equidistribution [electronic resource]: Sato-Tate Theorems for Finite-Field Mellin Transforms / Nicholas M. Katz.
개인저자	Katz, Nicholas M.
발행사항	Princeton: Princeton University Press, 2012.
형태사항	1 online resource (213 p.).
기타형태 저록	Print version: Katz, Nicholas M. Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms Princeton : Princeton University Press,c2012 9780691153315
ISBN	9781400842704 (electronic bk.) 1400842700 (electronic bk.) 1283379961 9781283379960
일반주기	Description based upon print version of record.
내용주기	Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Overview; Chapter 2. Convolution of Perverse Sheaves; Chapter 3. Fibre Functors; Chapter 4. The Situation over a Finite Field; Chapter 5. Frobenius Conjugacy Classes; Chapter 6. Group-Theoretic Facts about Ggeom and Garith; Chapter 7. The Main Theorem; Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility; Chapter 9. Autodualities and Signs; Chapter 10. A First Construction of Autodual Objects; Chapter 11. A Second Construction of Autodual Objects; Chapter 12. The Previous Construction in the Nonsplit Case; Chapter 13. Results of Goursat-Kolchin-Ribet TypeChapter 14. The Case of SL(2); the Examples of Evans and Rudnick; Chapter 15. Further SL(2) Examples, Based on the Legendre Family; Chapter 16. Frobenius Tori and Weights; Getting Elements of Garith; Chapter 17. GL(n) Examples; Chapter 18. Symplectic Examples; Chapter 19. Orthogonal Examples, Especially SO(n) Examples; Chapter 20. GL(n)xGL(n)x...xGL(n) Examples; Chapter 21. SL(n) Examples, for n an Odd Prime; Chapter 22. SL(n) Examples with Slightly Composite n; Chapter 23. Other SL(n) Examples; Chapter 24. An O(2n) Example Chapter 25. G2 Examples: the Overall StrategyChapter 26. G2 Examples: Construction in Characteristic Two; Chapter 27. G2 Examples: Construction in Odd Characteristic; Chapter 28. The Situation over Z: Results; Chapter 29. The Situation over Z: Questions; Chapter 30. Appendix: Deligne's Fibre Functor; Bibliography;
요약	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.
일반주제명	Algebro-geometric. Mathematics. Mellin transform. Convolutions (Mathematics) Sequences (Mathematics) MATHEMATICS / Functional Analysis
분류기호(DDC)	515.723
언어	영어
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