## Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116) |

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.
- Arithmetic Moduli of Elliptic Curves. (AM-108). [Paperback]
- Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180). [Hardcover and Paperback]
- Exponential Sums and Differential Equations. (AM-124). [Paperback]
- Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159). [Paperback]
- Rigid Local Systems. (AM-139). [Paperback]
- Twisted L-Functions and Monodromy. (AM-150). [Paperback]
- Annals of Mathematics Studies
Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors
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