ENGLISH

Exponential sums and differential equations

By Nicholas M. Katz

Book information

Publisher
Princeton University Press
Year
1990
ISBN
0691085986, 9780691085999, 9780691085982, 0691085994
LCC
QA246.7 .K38 1990
Open Library ID
OL1875004M
Language
english
Format
DJVU
Filesize
2 MB (2572190 bytes)
Series
Annals of mathematics studies 124
Pages
439\439
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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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