On multiple polylogarithms in characteristic p: v-adic vanishing versus ∞-adic Eulerianness

2015/11/11 by Chieh-Yu Chang, Chang, Chieh-Yu, Yoshinori Mishiba +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1511.03490

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 ∞-adic counterpart being Eulerian. This reveals a nontrivial connection between the v-adic and ∞-adic worlds in positive characteristic.

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• On finite Carlitz multiple polylogarithms

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