Zeta Values and Integral Representations in Characteristic p

Having an integral representation for a function means being able to write that function as a complex line integral of some (hopefully simple) function. In number theory, integral representations allow us to prove important properties of zeta functions and L-functions, such as functional equations and analytic continuations. My work focuses on properties of zeta values, L-functions and multiple zeta values in the characteristic-p function field setting. Because we're working in characteristic p, meaningful measures and integration theory are difficult to describe, so in general we don't have integral representations of these functions. I will describe some of my recent work which seeks to give an algebraic alternative to integral representations for these special values. This allows us to prove new properties for these values, such as describing new linear relations between them.

Bio
https://www2.latech.edu/~ngreen/