On ∞-adic and v-adic multiple zeta functions in positive characteristic

Abstract

In this paper, we pursue positive characteristic analogs of the results of Furusho, Komori, Matsumoto, and Tsumura on [Formula: see text]-adic multiple [Formula: see text]-functions. We consider [Formula: see text]-adic and [Formula: see text]-adic multiple zeta functions concerned by Anglès, Ngo Dac, and Tavares Ribeiro. Our main results in this paper consist of: (1) integral expressions of special values of [Formula: see text]-adic multiple zeta functions, (2) integral expressions of [Formula: see text]-adic multiple zeta functions themselves that are similar to those of [Formula: see text]-adic multiple [Formula: see text]-functions, (3) Kummer-type congruences for the special values of [Formula: see text]-adic multiple zeta functions at integers, (4) relationships between special values of [Formula: see text]-adic and those of [Formula: see text]-adic multiple zeta functions at negative integers, and (5) orthogonal properties of multiple zeta functions and multiple zeta star functions.