Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic

Abstract

Pellarin introduced the deformation of multiple zeta values of Thakur as elements over Tate algebras. In this paper, we relate these values to a certain coordinate of the logarithm of a higher dimensional Drinfeld module over the Tate algebra which we will introduce. Moreover, we define multiple polylogarithms in our setting and represent deformation of multiple zeta values as a linear combination of multiple polylogarithms. As an application of our results, we also write Dirichlet-Goss multiple $L$-values as a linear combination of twisted multiple polylogarithms at algebraic points.