Exponential Sums and Differential Equations

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 the author

Nicholas M. Katz

Summary

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).

Product details

• Authors: Nicholas Katz, Nicholas M. Katz
• Assisted by: Phillip Griffiths (Editor), Nicholas M. Katz (Editor), John N. Mather (Editor)
• Publisher: University Presses
• Languages: English
• Product format: Paperback / Softback
• Released: 21.09.1990
• EAN: 9780691085999
• ISBN: 978-0-691-08599-9
• No. of pages: 448
• Weight: 624 g
• Series: Annals of Mathematics Studies; Annals of Mathematics Studies
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / Differential Equations / General, MATHEMATICS / Number Theory, Number Theory, Differential calculus & equations, Differential calculus and equations