On Multiple Polylogarithms in Characteristic $p$: $v$-Adic Vanishing Versus $\infty$-Adic Eulerianness. (10th July 2017)

• Record Type: Journal Article
• Authors: Chang, Chieh-Yu; Mishiba, Yoshinori
• Is Part Of: International mathematics research notices. Volume 2019:Number 3(2019)
• Page Start: 923
• Page End: 947
• Publication Date: 2017-07-10
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx151
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: In this article, we give a simultaneous vanishing principle for the $v$ -adic Carlitz multiple polylogarithms (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.