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Exponential sums and differential equations /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Katz, Nicholas M., 1943-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 1990.
Colección:Annals of mathematics studies ; no. 124.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Katz, Nicholas M.,  |d 1943- 
245 1 0 |a Exponential sums and differential equations /  |c by Nicholas M. Katz. 
260 |a Princeton, N.J. :  |b Princeton University Press,  |c 1990. 
300 |a 1 online resource 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a Annals of mathematics studies ;  |v no. 124 
504 |a Includes bibliographical references (pages 425-430). 
505 0 |a Cover; Title; Copyright; Contents; Introduction; Chapter 1- Results from Representation Theory; 1.0-1.6 Statements of the main results; 1.7 The proofs; 1.8 Appendix: direct sums and tensor products; Chapter 2- D.E.'s and D-modules; 2.1 The basic set-up; 2.2 Torsors and lifting problems; 2.3 Relation to transcendence; 2.4 Behavior of Ggal under specialization; 2.5 Specialization of morphisms; 2.6 Direct sums and tensor products; 2.7 A basic trichotomy; 2.8 The main D.E. theorem; 2.9 Generalities on D-modules on curves; 2.10 Some equations on A^1, with a transition to Gm. 
505 8 |a 2.10.16 Location of the singularities of a Fourier Transform2.11 Systematic study of equations on Gm; Chapter 3- The generalized hypergeometric equation; 3.1 Basic definitions; 3.2-3.3 Basic results about irreducibility and contiguity; 3.4 Duality; 3.5 The case n= m; Lie irreducibility, rigidity, Belyi and Kummer induction; 3.6 The case n `"m; 3.7 Intrinsic characterization; rigidity for n `"m; 3.8 Direct sums, tensor products, and Kummer inductions; Chapter 4 Detailed analysis of the exceptional cases; 4.0 Eliminating a few cases; 4.1 The G2 case. 
505 8 |a 4.2 The Spin(7), PSL(3) and SL(2)xSL(2)xSL(2) cases4.3 The PSL(3) case: detailed analysis; 4.4 The Spin(7) case: detailed analysis; 4.5 The SL(2)xSL(2)xSL(2) case; 4.6 The SL(3)xSL(3) case; Chapter 5- Convolution of D-modules; 5.1 Generalities; 5.2 Convolution on Gm and Fourier Transform on A^1; 5.3 Convolution of hypergeometrics on Gm; 5.4 Motivic interpretation of hypergeometrics of type (n, n); 5.5 Application to Grothendieck's p-curvature conjecture; Chapter 6- Fourier transforms of Kummer pullbacks of hypergeometrics; 6.1 Some D.E.'s on A^1 as Kummer pullbacks of hypergeometrics. 
505 8 |a 6.2 Fourier transforms of Kummer pullbacks of hypergeometrics: a remarkable stability6.3 convolution of hypergeometrics with nondisjoint exponents, via a modified sort of hypergeometric; 6.4 Applications to Fourier transforms of Kummer pullbacks of hypergeometrics; Chapter 7- The l-adic theory; 7.1 Exceptional sets of primes; 7.2 l-adic analogue of the main D.E. theorem 2.8.1; 7.3 Construction of irreducible sheaves via Fourier transform; 7.4 Local monodromy of Fourier transforms d'apres Laumon; 7.5 ""Numerical"" explicitation of Lauman's results. 
505 8 |a 7.6 Pseudoreflection examples and applications7.7 A highest slope application; 7.8 Fourier transform-stable classes of sheaves; 7.9 Fourier transforms of tame pseudoreflection sheaves; 7.10 Examples; 7.11 Sato-Tate laws for one-variable exponential sums; 7.12 Special linear examples; 7.13 Symplectic examples; 7.14 Orthogonal examples; Chapter 8- l-adic hypergeometrics; 8.1 Rapid review of perversity, Fourier transform, and convolution; 8.2 Definition of hypergeometric complexes and hypergeometric sums over finite fields; 8.3 Variant: hypergeometric complexes over algebraically closed fields. 
590 |a JSTOR  |b Books at JSTOR All Purchased 
590 |a JSTOR  |b Books at JSTOR Evidence Based Acquisitions 
590 |a JSTOR  |b Books at JSTOR Demand Driven Acquisitions (DDA) 
650 0 |a Exponential sums. 
650 0 |a Differential equations. 
650 6 |a Sommes exponentielles. 
650 6 |a Équations différentielles. 
650 7 |a MATHEMATICS  |x Differential Equations  |x General.  |2 bisacsh 
650 7 |a Differential equations.  |2 fast  |0 (OCoLC)fst00893446 
650 7 |a Exponential sums.  |2 fast  |0 (OCoLC)fst00918663 
653 0 |a Differential equations 
653 0 |a Exponential sums 
776 0 8 |i Print version:  |a Katz, Nicholas M., 1943-  |t Exponential sums and differential equations.  |d Princeton, N.J. : Princeton University Press, 1990  |w (DLC) 90034934 
830 0 |a Annals of mathematics studies ;  |v no. 124. 
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