Exponential Sums and Differential Equations
eBook - PDF

Exponential Sums and Differential Equations

  1. 445 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Exponential Sums and Differential Equations

About this book

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.

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Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Introduction
  6. Chapter 1- Results from Representation Theory
  7. Chapter 2- D.E.'s and D-modules
  8. Chapter 3- The generalized hypergeometric equation
  9. Chapter 4 Detailed analysis of the exceptional cases
  10. Chapter 5- Convolution of D-modules
  11. Chapter 6- Fourier transforms of Kummer pullbacks of hypergeometrics
  12. Chapter 7- The l-adic theory
  13. Chapter 8- l-adic hypergeometrics
  14. Chapter 9 G2 examples, Fourier transforms and hypergeometrics
  15. Chapter 10- l-adic exceptional cases
  16. Chapter 11- Reductive tannakian categories
  17. Chapter 12- Fourier universality
  18. Chapter 13- Stratifications and convolution
  19. Chapter 14- The fundamental comparison theorems
  20. References

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Yes, you can access Exponential Sums and Differential Equations by Nicholas M. Katz in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.