Taylor coefficients of Anderson-Thakur series and explicit formulae

Abstract

For each positive characteristic multiple zeta value (defined by Thakur [T04]), the first and third authors in [CM19b] constructed a t-module together with a specific algebraic point such that a chosen coordinate of the logarithmic vector of the algebraic point is a rational multiple of that multiple zeta value. The objective of this paper is to introduce t-motivic multiple zeta values and t-motivic Carlitz multiple polylogarithms, and use their Taylor coefficients to give explicit formulae for all of the coordinates of this logarithmic vector.

Algebra structure of multiple zeta values in positive characteristic

“…Remark 2.3.2. In fact, all coordinates of log Gs,u (v s,u ) can be written explicitly in [CGM19], and the tractable coordinates (see Definition 5.1.4) of log Gs,u (v s,u ) v are given explicitly in [CM19].…”