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Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz



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Autore: Katz Nicholas M. <1943-> Visualizza persona
Titolo: Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz Visualizza cluster
Pubblicazione: Princeton ; ; Oxford, : Princeton University Press, c2012
Edizione: Course Book
Descrizione fisica: 1 online resource (213 p.)
Disciplina: 515/.723
Soggetto topico: Mellin transform
Convolutions (Mathematics)
Sequences (Mathematics)
Soggetto non controllato: ArtinГchreier reduced polynomial
Emanuel Kowalski
EulerАoincar formula
Frobenius conjugacy class
Frobenius conjugacy
Frobenius tori
GoursatЋolchinВibet theorem
Kloosterman sheaf
Laurent polynomial
Legendre
Mellin transform
Pierre Deligne
Ron Evans
Tannakian category
Tannakian groups
Zeeev Rudnick
algebro-geometric
autodual objects
autoduality
characteristic two
connectedness
dimensional objects
duality
equidistribution
exponential sums
fiber functor
finite field Mellin transform
finite field
finite fields
geometrical irreducibility
group scheme
hypergeometric sheaf
interger monic polynomials
isogenies
lie-irreducibility
lisse
middle convolution
middle extension sheaf
monic polynomial
monodromy groups
noetherian connected scheme
nonsplit form
nontrivial additive character
number theory
odd characteristic
odd prime
orthogonal case
perverse sheaves
polynomials
pure weight
semisimple object
semisimple
sheaves
signs
split form
supermorse
theorem
theorems
Classificazione: SI 830
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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 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
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.
Titolo autorizzato: Convolution and equidistribution  Visualizza cluster
ISBN: 1-283-37996-1
9786613379962
1-4008-4270-0
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910789730903321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of mathematics studies ; ; no. 180.