Exponential Sums and Differential Equations. (AM-124) (Annals of Mathematics Studies, 124) - Softcover

Katz, Nicholas M.

Softcover

ISBN 10: 0691085994 ISBN 13: 9780691085999

Publisher: Princeton University Press, 1990

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Princeton University Press
• Publication date: 1990
• Language: English
• ISBN 10: 0691085994
• ISBN 13: 9780691085999
• Binding: Paperback
• Number of pages: 444