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

Nicholas M. Katz (Autor)

Buch | Softcover

448 Seiten

1990
Princeton University Press (Verlag)
978-0-691-08599-9 (ISBN)

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Deals with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. This 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).

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.

*Frontmatter, pg. i*Contents, pg. v*Introduction, pg. 1*CHAPTER 1. Results from Representation Theory, pg. 9*CHAPTER 2. D.E.'s and D-modules, pg. 31*CHAPTER 3. The Generalized Hypergeometric Equation, pg. 92*CHAPTER 4. Detailed Analysis of the Exceptional Cases, pg. 122*CHAPTER 5. Convolution of D-modules, pg. 161*CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics, pg. 178*CHAPTER 7. The l- adic Theory, pg. 193*CHAPTER 8. l-adic Hypergeometrics, pg. 251*CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics, pg. 320*CHAPTER 10. l -adic Exceptional Cases, pg. 332*CHAPTER 11. Reductive Tannakian Categories, pg. 352*CHAPTER 12. Fourier Universality, pg. 363*CHAPTER 13. Stratifications and Convolution, pg. 384*CHAPTER 14. The Fundamental Comparison Theorems, pg. 402*References, pg. 425

Erscheint lt. Verlag	21.9.1990
Reihe/Serie	Annals of Mathematics Studies
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	624 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	0-691-08599-4 / 0691085994
ISBN-13	978-0-691-08599-9 / 9780691085999
Zustand	Neuware