Number Theory Seminar

Date: December 8, 2022

Time: 1:00PM - 2:00PM

Location: BLOC 302

Speaker: Yen-Tsung Chen, Penn State University

Title: On Thakur's basis conjecture for multiple zeta values in positive characteristic

Abstract: Classical multiple zeta values (MZV's) are generalizations of special values of the Riemann zeta function at positive integers. The machinery of regularized double shuffle relations produces many linear relations among MZV's. There is a famous conjecture of Zagier predicting the dimension of the vector space spanned by MZV's of the same weight. Furthermore, due to the numerical computation, Hoffman proposed a conjectural basis for the space in question. In the parallel but quite different world, namely the global function fields, Thakur introduced an analogue of classical MZV's in the function field setting. In this talk, we give affirmative answers to the conjectures of Todd and Thakur which are analogues of the conjectures of Zagier and Hoffman respectively for MZV's in positive characteristic. This is joint work with Chieh-Yu Chang and Yoshinori Mishiba.