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Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| 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 |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910789730903321 |
Katz Nicholas M. <1943->
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| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mathematical Analysis and Analytic Number Theory 2019
| Mathematical Analysis and Analytic Number Theory 2019 |
| Autore | Srivastava Rekha |
| Pubbl/distr/stampa | Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2021 |
| Descrizione fisica | 1 online resource (318 p.) |
| Soggetto topico |
Mathematics & science
Research & information: general |
| Soggetto non controllato |
analytic functions
Appell-Bessel functions ArcTan and ArcTanh functions asymptotics Bessel functions bi-close-to-convex functions cardioid domain Catalan's constant Chebyshev polynomials circular domain close-to-convex functions close-to-convexity closed form closure property coefficient estimates combinatorial partition-theoretic identities conic domain convergence theorems convex functions convexity convolution cotangent sum Dedekind sum delta sequence determinant differential operator distortion distribution Euler sums Euler's pentagonal number theorem exponential sums Fibonacci number Fox-Wright function fractional Laplacian functions with positive real part gamma function and its extension generalized Lupaş operators generating functions Hadamard product Hankel determinant Hankel matrix Hardy space harmonic numbers harmonic univalent functions hyper-Bessel functions hypergeometric function and its extensions integral expressions integral representation integral representations inverse Jacobi's triple-product identity Janowski functions Korovkin's type theorem Lambert series laplace and other integral transforms lemniscate of Bernoulli Hankel determinant Lucas number m-fold symmetric functions Mersenne number modular transformation multivalent functions multivariable R-functions p-valent analytic function partial fractions periodic tridiagonal Toeplitz matrix Pochhammer symbol and its extensions q analogue q-Bernardi integral operator q-close-to-convex functions q-convex functions q-integral operator q-product identities q-Ruschweyh differential operator q-starlike functions quasi-Hadamard Ramanujan's theta functions reciprocals riemann zeta function Riesz fractional derivative Rogers-Ramanujan continued fraction Rogers-Ramanujan identities Schur's second partition theorem Schur's, the Göllnitz-Gordon's and the Göllnitz's partition identities second Hankel determinant Sherman-Morrison-Woodbury formula special functions starlike function starlike functions starlikeness subordinate subordination subordinations theta-function identities Toeplitz matrix Trigamma function umbral methods univalent function univalent functions Voronovskaya type theorem with symmetric conjecture point τ-Gauss hypergeometric function and its extensions τ-Kummer hypergeometric function |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910557507003321 |
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Srivastava Rekha
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| Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||