Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) /

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 direction...

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Detalles Bibliográficos
Autor principal: Katz, Nicholas M. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2012]
Edición:Course Book.
Colección:Book collections on Project MUSE.
Temas:
Sequences (Mathematics)
Mellin transform.
Convolutions (Mathematics)
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • 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 Type
  • CHAPTER 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) x GL(n) x ... x GL(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 Strategy
  • CHAPTER 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
  • Index

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