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

Date: 
Thu, Apr 1, 2004
Author: 
Sergei Konyagin
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.
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