Exponential Sums and Differential Equations. (AM-124), Volume 124 /

Exponential Sums and Differential Equations. (AM-124), Volume 124 / / Nicholas M. Katz.

This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of e...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Katz, Nicholas M.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1991
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 124
Online Access:
Physical Description:1 online resource (448 p.)
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100 1 |a Katz, Nicholas M.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Exponential Sums and Differential Equations. (AM-124), Volume 124 /  |c Nicholas M. Katz. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1991 
300 |a 1 online resource (448 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 0 |a Annals of Mathematics Studies ;  |v 124 
505 0 0 |t Frontmatter --   |t Contents --   |t Introduction --   |t CHAPTER 1. Results from Representation Theory --   |t CHAPTER 2. D.E.'s and D-modules --   |t CHAPTER 3. The Generalized Hypergeometric Equation --   |t CHAPTER 4. Detailed Analysis of the Exceptional Cases --   |t CHAPTER 5. Convolution of D-modules --   |t CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics --   |t CHAPTER 7. The ℓ- adic Theory --   |t CHAPTER 8. ℓ-adic Hypergeometrics --   |t CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics --   |t CHAPTER 10. ℓ -adic Exceptional Cases --   |t CHAPTER 11. Reductive Tannakian Categories --   |t CHAPTER 12. Fourier Universality --   |t CHAPTER 13. Stratifications and Convolution --   |t CHAPTER 14. The Fundamental Comparison Theorems --   |t References 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Differential equations. 
650 0 |a Exponential sums. 
650 7 |a MATHEMATICS / Differential Equations / General.  |2 bisacsh 
653 |a Adjoint representation. 
653 |a Algebraic geometry. 
653 |a Algebraic integer. 
653 |a Algebraically closed field. 
653 |a Automorphism. 
653 |a Base change. 
653 |a Bernard Dwork. 
653 |a Big O notation. 
653 |a Bijection. 
653 |a Calculation. 
653 |a Characteristic polynomial. 
653 |a Codimension. 
653 |a Coefficient. 
653 |a Cohomology. 
653 |a Comparison theorem. 
653 |a Complex manifold. 
653 |a Conjugacy class. 
653 |a Connected component (graph theory). 
653 |a Convolution. 
653 |a Determinant. 
653 |a Diagram (category theory). 
653 |a Differential Galois theory. 
653 |a Differential equation. 
653 |a Dimension (vector space). 
653 |a Dimension. 
653 |a Direct sum. 
653 |a Divisor. 
653 |a Eigenvalues and eigenvectors. 
653 |a Endomorphism. 
653 |a Equation. 
653 |a Euler characteristic. 
653 |a Existential quantification. 
653 |a Exponential sum. 
653 |a Fiber bundle. 
653 |a Field of fractions. 
653 |a Finite field. 
653 |a Formal power series. 
653 |a Fourier transform. 
653 |a Fundamental group. 
653 |a Fundamental representation. 
653 |a Galois extension. 
653 |a Galois group. 
653 |a Gauss sum. 
653 |a Generic point. 
653 |a Group theory. 
653 |a Homomorphism. 
653 |a Hypergeometric function. 
653 |a Identity component. 
653 |a Identity element. 
653 |a Integer. 
653 |a Irreducibility (mathematics). 
653 |a Irreducible representation. 
653 |a Isogeny. 
653 |a Isomorphism class. 
653 |a L-function. 
653 |a Laurent polynomial. 
653 |a Lie algebra. 
653 |a Logarithm. 
653 |a Mathematical induction. 
653 |a Matrix coefficient. 
653 |a Maximal compact subgroup. 
653 |a Maximal torus. 
653 |a Mellin transform. 
653 |a Monic polynomial. 
653 |a Monodromy theorem. 
653 |a Monodromy. 
653 |a Monomial. 
653 |a Natural number. 
653 |a Normal subgroup. 
653 |a P-adic number. 
653 |a Permutation. 
653 |a Polynomial. 
653 |a Prime number. 
653 |a Pullback. 
653 |a Quotient group. 
653 |a Reductive group. 
653 |a Regular singular point. 
653 |a Representation theory. 
653 |a Ring homomorphism. 
653 |a Root of unity. 
653 |a Scientific notation. 
653 |a Set (mathematics). 
653 |a Sheaf (mathematics). 
653 |a Special case. 
653 |a Subcategory. 
653 |a Subgroup. 
653 |a Subring. 
653 |a Subset. 
653 |a Summation. 
653 |a Surjective function. 
653 |a Symmetric group. 
653 |a Tensor product. 
653 |a Theorem. 
653 |a Theory. 
653 |a Three-dimensional space (mathematics). 
653 |a Torsor (algebraic geometry). 
653 |a Trichotomy (mathematics). 
653 |a Unitarian trick. 
653 |a Unitary group. 
653 |a Variable (mathematics). 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
776 0 |c print  |z 9780691085999 
856 4 0 |u https://doi.org/10.1515/9781400882434 
856 4 0 |u https://www.degruyter.com/isbn/9781400882434 
856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400882434/original 
912 |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999  |c 1927  |d 1999 
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