Exponential sums and twisted multiplicativity
ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR
Date
Thursday, January 7, 2021 14:00 - 15:00
Speaker
Emmanuel Kowalski (ETH Zürich)
Location
https://mathseminars.org/seminar/AGNTISTA
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tim Browning
Contact
Birgit Oosthuizen-Noczil
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)