Multiple zeta values in positive characteristic I : Zagier-Hoffman's Conjectures

Abstract

Zagier-Hoffman’s conjectures in the classical setting on multiple zeta values over Q of Euler and Euler sums are still open. As analogues of the classical case, multiple zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada. In this talk, we determine the dimension and a basis of the span of all alternating multiple zeta values over the rational function field by finding all linear relations among them. As a consequence, we completely establish Zagier-Hoffman’s conjectures in positive characteristic formulated by Todd and Thakur which predict the dimension and an explicit basis of the span of multiple zeta values of Thakur of fixed weight.