On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic Eulerianness

Abstract

In this paper, we give a simultaneous vanishing principle for the $v$-adic Carlitz multiple polylogarithms (abbreviated as CMPLs) at algebraic points, where $v$ is a finite place of the rational function field over a finite field. This principle establishes the fact that the $v$-adic vanishing of CMPLs at algebraic points is equivalent to its $\infty$-adic counterpart being Eulerian. This reveals a nontrivial connection between the $v$-adic and $\infty$-adic worlds in positive characteristic.

Title changed; Sec. 4 on analytic continuation added; Final version to appear in IMRN

References in corpus (3)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• Linear independence of monomials of multizeta values in positive characteristic
• Fundamentals of p-adic multiple L-functions and evaluation of their special values

Cited by in corpus (1)

• On finite Carlitz multiple polylogarithms