Exponential Sums Over Multiplicative Groups in Fields of Prime Order and Related Combinatorial Problems

Author: 
Sergei Konyagin
Date: 
Thu, Apr 1, 2004
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

Let $ p $ be a prime. The main subject of my talks is the estimation of exponential sums over an arbitrary subgroup $ G $ of the multiplicative group $ {\mathbb Z}^*_p $:

$$S(a, G) = \sum_{x\in G} \exp(2\pi iax/p),	a \in \mathbb Z_p.$$

These sums have numerous applications in additive problems modulo $ p $, pseudo-random generators, coding theory, theory of algebraic curves and other problems.

Notes: