Download or read book Gauss Sums, Kloosterman Sums, and Monodromy Groups written by Nicholas M. Katz and published by Princeton University Press. This book was released on 1988 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.