Exponential sums in coding theory, combinatorics, and number theory
by
Carlos Julio Moreno
City University of New York (Graduate Center, Baruch College)

Combinatorial harmonic analysis on finite rings and fields underlies the most fundamental applications of exponential sums to coding theory, combinatorics, and number theory. This is particularly true of results in coding theory which describe the weight distribution of certain binary codes as well as in the derivation of optimal properties of Ramanujan graphs. In number theory, since the time of Gauss, exponential sums have appeared in the study of reciprocity laws. More recently, in their guise as root numbers, they play a central role in the modern study of automorphic forms. In our talk we shall describe some of these applications.

Date received: March 10, 1999

Copyright © 1999 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 # cabw-93.