Exponential sums and differential equations
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 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.
种类:
年:
1990
出版社:
Princeton University Press
语言:
english
页:
439
ISBN 10:
0691085994
ISBN 13:
9780691085999
系列:
Annals of mathematics studies 124
文件:
DJVU, 2.45 MB
IPFS:
,
english, 1990