Exponential sums modulo prime powers
by
Todd Cochrane
Kansas State University
Coauthors: Zhiyong Zheng (Tsinghua University)

We discuss our recent work on obtaining upper bounds and explicit formulae for exponential sums of the type \sum_x e_p^m(f(x)) and \sum_x \chi(x) e_p^m(f(x)), x running from 1 to p^m, where p^m is a prime power, \chi is a multiplicative character mod p^m and f(x) is a polynomial or more generally, a rational function. Of particular interest is the polynomial f=ax^d+bx, Kloosterman and Salie sums, and n-dimensional Kloosterman sums. The classical upper bound of Hua is sharpened and generalized, and a new method is introduced for untwisting mixed exponential sums.

Date received: March 8, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-60.