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[null,"1.","Record Nr.",null,"UNINA9910968930703321"]
[null,null,"Autore",null,"Katz Nicholas M. <1943->"]
[null,null,"Titolo",null,"Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz"]
[null,null,"Pubbl/distr/stampa",null,"Princeton ; ; Oxford, : Princeton University Press, c2012"]
[null,null,"ISBN",null,"9786613379962"]
[{"$nulls":4},"9781283379960"]
[{"$nulls":4},"1283379961"]
[{"$nulls":4},"9781400842704"]
[{"$nulls":4},"1400842700"]
[null,null,"Edizione",null,"[Course Book]"]
[null,null,"Descrizione fisica",null,"1 online resource (213 p.)"]
[null,null,"Collana",null,"Annals of mathematics studies ; ; no. 180"]
[null,null,"Classificazione",null,"SI 830"]
[null,null,"Disciplina",null,"515/.723"]
[null,null,"Soggetti",null,"Mellin transform"]
[{"$nulls":4},"Convolutions (Mathematics)"]
[{"$nulls":4},"Sequences (Mathematics)"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Front matter -- 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 "]
[{"$nulls":4},"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"]
[null,null,null,"Sommario/riassunto","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."]