Number Theory Seminar

Date: October 13, 2022

Time: 2:30PM - 3:30PM

Location: BLOC 302

Speaker: Nathan Green, Louisiana Tech University

Title: A motivic pairing and applications

Abstract: We describe our recent result on several pairings between the t-motive and the dual t-motive associated to a t-module. Specializations of these pairings allow us to give explicit formulas for the exponential and logarithmic functions of the t-module. We also explain a few applications of variations of these pairings, such as a Mellin transform-like formula for Carlitz zeta values. We describe possible generalizations of this formula to higher rank Drinfeld modules, which is a current work in progress. Time permitting, we will also explain the connection between these pairings and a noncommutative factorization of the Carlitz exponential which gives multiple zeta values.