Exponential sums and twisted multiplicativity

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

The additive exponential sums associated to an integral polynomial
satisfy a property of twisted-multiplicativity. Using this, it is
possible to exploit properties of these sums over finite fields to gain
some understanding of the sums modulo all integers. This involves a
fine interplay of algebraic methods and analytic techniques. The
explain will describe some of these, and explain in particular how to
deduce that the mean value of these exponential sums vanishes for
suitably generic polynomials.

(Joint work with K. Soundararajan)