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
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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
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Physical Description:1 online resource (448 p.)
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spelling Katz, Nicholas M., author. aut http://id.loc.gov/vocabulary/relators/aut
Exponential Sums and Differential Equations. (AM-124), Volume 124 / Nicholas M. Katz.
Princeton, NJ : Princeton University Press, [2016]
©1991
1 online resource (448 p.)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 124
Frontmatter -- Contents -- Introduction -- CHAPTER 1. Results from Representation Theory -- CHAPTER 2. D.E.'s and D-modules -- CHAPTER 3. The Generalized Hypergeometric Equation -- CHAPTER 4. Detailed Analysis of the Exceptional Cases -- CHAPTER 5. Convolution of D-modules -- CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics -- CHAPTER 7. The ℓ- adic Theory -- CHAPTER 8. ℓ-adic Hypergeometrics -- CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics -- CHAPTER 10. ℓ -adic Exceptional Cases -- CHAPTER 11. Reductive Tannakian Categories -- CHAPTER 12. Fourier Universality -- CHAPTER 13. Stratifications and Convolution -- CHAPTER 14. The Fundamental Comparison Theorems -- References
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
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.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Differential equations.
Exponential sums.
MATHEMATICS / Differential Equations / General. bisacsh
Adjoint representation.
Algebraic geometry.
Algebraic integer.
Algebraically closed field.
Automorphism.
Base change.
Bernard Dwork.
Big O notation.
Bijection.
Calculation.
Characteristic polynomial.
Codimension.
Coefficient.
Cohomology.
Comparison theorem.
Complex manifold.
Conjugacy class.
Connected component (graph theory).
Convolution.
Determinant.
Diagram (category theory).
Differential Galois theory.
Differential equation.
Dimension (vector space).
Dimension.
Direct sum.
Divisor.
Eigenvalues and eigenvectors.
Endomorphism.
Equation.
Euler characteristic.
Existential quantification.
Exponential sum.
Fiber bundle.
Field of fractions.
Finite field.
Formal power series.
Fourier transform.
Fundamental group.
Fundamental representation.
Galois extension.
Galois group.
Gauss sum.
Generic point.
Group theory.
Homomorphism.
Hypergeometric function.
Identity component.
Identity element.
Integer.
Irreducibility (mathematics).
Irreducible representation.
Isogeny.
Isomorphism class.
L-function.
Laurent polynomial.
Lie algebra.
Logarithm.
Mathematical induction.
Matrix coefficient.
Maximal compact subgroup.
Maximal torus.
Mellin transform.
Monic polynomial.
Monodromy theorem.
Monodromy.
Monomial.
Natural number.
Normal subgroup.
P-adic number.
Permutation.
Polynomial.
Prime number.
Pullback.
Quotient group.
Reductive group.
Regular singular point.
Representation theory.
Ring homomorphism.
Root of unity.
Scientific notation.
Set (mathematics).
Sheaf (mathematics).
Special case.
Subcategory.
Subgroup.
Subring.
Subset.
Summation.
Surjective function.
Symmetric group.
Tensor product.
Theorem.
Theory.
Three-dimensional space (mathematics).
Torsor (algebraic geometry).
Trichotomy (mathematics).
Unitarian trick.
Unitary group.
Variable (mathematics).
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691085999
https://doi.org/10.1515/9781400882434
https://www.degruyter.com/isbn/9781400882434
Cover https://www.degruyter.com/document/cover/isbn/9781400882434/original
language English
format eBook
author Katz, Nicholas M.,
Katz, Nicholas M.,
spellingShingle Katz, Nicholas M.,
Katz, Nicholas M.,
Exponential Sums and Differential Equations. (AM-124), Volume 124 /
Annals of Mathematics Studies ;
Frontmatter --
Contents --
Introduction --
CHAPTER 1. Results from Representation Theory --
CHAPTER 2. D.E.'s and D-modules --
CHAPTER 3. The Generalized Hypergeometric Equation --
CHAPTER 4. Detailed Analysis of the Exceptional Cases --
CHAPTER 5. Convolution of D-modules --
CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics --
CHAPTER 7. The ℓ- adic Theory --
CHAPTER 8. ℓ-adic Hypergeometrics --
CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics --
CHAPTER 10. ℓ -adic Exceptional Cases --
CHAPTER 11. Reductive Tannakian Categories --
CHAPTER 12. Fourier Universality --
CHAPTER 13. Stratifications and Convolution --
CHAPTER 14. The Fundamental Comparison Theorems --
References
author_facet Katz, Nicholas M.,
Katz, Nicholas M.,
author_variant n m k nm nmk
n m k nm nmk
author_role VerfasserIn
VerfasserIn
author_sort Katz, Nicholas M.,
title Exponential Sums and Differential Equations. (AM-124), Volume 124 /
title_full Exponential Sums and Differential Equations. (AM-124), Volume 124 / Nicholas M. Katz.
title_fullStr Exponential Sums and Differential Equations. (AM-124), Volume 124 / Nicholas M. Katz.
title_full_unstemmed Exponential Sums and Differential Equations. (AM-124), Volume 124 / Nicholas M. Katz.
title_auth Exponential Sums and Differential Equations. (AM-124), Volume 124 /
title_alt Frontmatter --
Contents --
Introduction --
CHAPTER 1. Results from Representation Theory --
CHAPTER 2. D.E.'s and D-modules --
CHAPTER 3. The Generalized Hypergeometric Equation --
CHAPTER 4. Detailed Analysis of the Exceptional Cases --
CHAPTER 5. Convolution of D-modules --
CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics --
CHAPTER 7. The ℓ- adic Theory --
CHAPTER 8. ℓ-adic Hypergeometrics --
CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics --
CHAPTER 10. ℓ -adic Exceptional Cases --
CHAPTER 11. Reductive Tannakian Categories --
CHAPTER 12. Fourier Universality --
CHAPTER 13. Stratifications and Convolution --
CHAPTER 14. The Fundamental Comparison Theorems --
References
title_new Exponential Sums and Differential Equations. (AM-124), Volume 124 /
title_sort exponential sums and differential equations. (am-124), volume 124 /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2016
physical 1 online resource (448 p.)
Issued also in print.
contents Frontmatter --
Contents --
Introduction --
CHAPTER 1. Results from Representation Theory --
CHAPTER 2. D.E.'s and D-modules --
CHAPTER 3. The Generalized Hypergeometric Equation --
CHAPTER 4. Detailed Analysis of the Exceptional Cases --
CHAPTER 5. Convolution of D-modules --
CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics --
CHAPTER 7. The ℓ- adic Theory --
CHAPTER 8. ℓ-adic Hypergeometrics --
CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics --
CHAPTER 10. ℓ -adic Exceptional Cases --
CHAPTER 11. Reductive Tannakian Categories --
CHAPTER 12. Fourier Universality --
CHAPTER 13. Stratifications and Convolution --
CHAPTER 14. The Fundamental Comparison Theorems --
References
isbn 9781400882434
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9783110442496
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callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA246
callnumber-sort QA 3246.7 K38 41990
url https://doi.org/10.1515/9781400882434
https://www.degruyter.com/isbn/9781400882434
https://www.degruyter.com/document/cover/isbn/9781400882434/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 512 - Algebra
dewey-full 512/.73
dewey-sort 3512 273
dewey-raw 512/.73
dewey-search 512/.73
doi_str_mv 10.1515/9781400882434
oclc_num 979633762
work_keys_str_mv AT katznicholasm exponentialsumsanddifferentialequationsam124volume124
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hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Exponential Sums and Differential Equations. (AM-124), Volume 124 /
container_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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