Arithmetic Geometry and Number Theory RTG Seminar: Burgess methods in new settings

Seminar | December 2 | 3:10-5 p.m. | 740 Evans Hall

 Lilliance Pierce, Duke

 Department of Mathematics

About 60 years ago, the Burgess method set a record for bounding short multiplicative character sums in one dimension. This talk will present a “Burgess method” for character sums in arbitrary dimensions, involving both additive and multiplicative characters, evaluated at appropriate polynomials. This includes an unexpected connection to the Vinogradov Mean Value Theorem.

In the pre-talk I will give some motivations for why bounds for “short" sums are particularly difficult, and particularly useful.