Exponential sums and twisted multiplicativity

Abstract: 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)

algebraic geometrynumber theory

Audience: researchers in the topic

Algebraic Geometry and Number Theory seminar - ISTA