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 a higher dimensional Drinfeld module over Tate algebras 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.

46 pages

References in corpus (2)

• The de Rham isomorphism for Drinfeld modules over Tate algebras
• A note on multiple zeta values in Tate algebras

Cited by in corpus (3)

• Hyperderivative power sums, Vandermonde matrices, and Carlitz multiplication coefficients
• Special values of Goss $L$-series attached to Drinfeld modules of rank 2
• Trivial multiple zeta values in Tate algebras