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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...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, NJ :
Princeton University Press,
[2012]
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| Edición: | Course Book. |
| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 008 | 190708s2012 nju o 00 0 eng d | ||
| 020 | |a 9781400842704 | ||
| 020 | |z 9780691153315 | ||
| 020 | |z 9780691153308 | ||
| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Katz, Nicholas M., |e author. | |
| 245 | 1 | 0 | |a Convolution and Equidistribution : |b Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) / |c Nicholas M. Katz. |
| 250 | |a Course Book. | ||
| 264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2012] | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 0000 | |
| 264 | 4 | |c ©[2012] | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Annals of Mathematics Studies ; |v 203 | |
| 500 | |a Description based upon print version of record. | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Introduction -- |t CHAPTER 1. Overview -- |t CHAPTER 2. Convolution of Perverse Sheaves -- |t CHAPTER 3. Fibre Functors -- |t CHAPTER 4. The Situation over a Finite Field -- |t CHAPTER 5. Frobenius Conjugacy Classes -- |t CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- |t CHAPTER 7. The Main Theorem -- |t CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- |t CHAPTER 9. Autodualities and Signs -- |t CHAPTER 10. A First Construction of Autodual Objects -- |t CHAPTER 11. A Second Construction of Autodual Objects -- |t CHAPTER 12. The Previous Construction in the Nonsplit Case -- |t CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- |t CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- |t CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- |t CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- |t CHAPTER 17. GL(n) Examples -- |t CHAPTER 18. Symplectic Examples -- |t CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- |t CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- |t CHAPTER 21. SL(n) Examples, for n an Odd Prime -- |t CHAPTER 22. SL(n) Examples with Slightly Composite n -- |t CHAPTER 23. Other SL(n) Examples -- |t CHAPTER 24. An O(2n) Example -- |t CHAPTER 25. G2 Examples: the Overall Strategy -- |t CHAPTER 26. G2 Examples: Construction in Characteristic Two -- |t CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- |t CHAPTER 28. The Situation over ℤ: Results -- |t CHAPTER 29. The Situation over ℤ: Questions -- |t CHAPTER 30. Appendix: Deligne's Fibre Functor -- |t Bibliography -- |t Index |
| 520 | |a 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. | ||
| 521 | |a Specialized. | ||
| 546 | |a English. | ||
| 588 | |a Description based on print version record. | ||
| 650 | 7 | |a Sequences (Mathematics) |2 fast |0 (OCoLC)fst01112884 | |
| 650 | 7 | |a Mellin transform. |2 fast |0 (OCoLC)fst01015759 | |
| 650 | 7 | |a Convolutions (Mathematics) |2 fast |0 (OCoLC)fst00877310 | |
| 650 | 0 | |a Sequences (Mathematics) | |
| 650 | 0 | |a Convolutions (Mathematics) | |
| 650 | 0 | |a Mellin transform. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/30702/ |
| 945 | |a Project MUSE - Custom Collection | ||