Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 (Annals of Mathematics Studies) by Nicholas M. Katz (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐exactly what I expected.

⭐This book contains very good applications of étale cohomology. It shows how to use modern arithmetic algebraic geometry to study classical sums in number theory.

⭐

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