有限多重ポリログとその関数等式 (Algebraic Number Theory and Related Topics 2016)

Abstract

This article is a research announcement of the results in [16] and [18]. Rosen generalized Kaneko-Zagier's A-fi nite multiple zeta values to Â- finite multiple zeta values (Â-FMZVs) p-adically in [14]. We introduce Â- finite multiple polylogarithms (Â-FMPs) which are multiple and p-adic generalizations of nite polylogarithms de ned by Elbaz-Vincent-Gangl as elements of a certain p-adic ring. Our Â-FMPs are also regarded as generalizations of Â-FMZVs in the sense that some of the special values of our Â-FMPs give Rosen's Â-FMZVs. Our main results are some fundamental functional relations for Â-FMPs including the multi-variable functional equation which is a generalization of Hoffman's duality.