On functional equations of finite multiple polylogarithms

2015/09/25 by Kenji Sakugawa, Shin-ichiro Seki, Sakugawa, Kenji +1 · 1 citation
Mathematics · #11B50 #11B68 #11M32 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B50 #msc:11B68 #msc:11M32

paper · pdf · doi:10.48550/arxiv.1509.07653

44 pages, 1 table

arxiv created 2016/02/22 · arxiv updated 2016/02/23

Abstract

Recently, several people study finite multiple zeta values (FMZVs) and finite polylogarithms (FPs). In this paper, we introduce finite multiple polylogarithms (FMPs), which are natural generalizations of FMZVs and FPs, and we establish functional equations of FMPs. As applications of these functional equations, we calculate special values of FMPs containing generalizations of congruences obtained by Meštrović, Z. W. Sun, Z. W. Sun-L. L. Zhao, and Tauraso-J. Zhao. We show supercongruences for certain generalized Bernoulli numbers and the Bernoulli numbers as an appendix.

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