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

2022/01/31 by Daichi Matsuzuki, Matsuzuki, Daichi
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.12953

openalex publication_date 2022/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper pursues positive characteristic analogues of the results of Furusho, Komori, Matsumoto and Tsumura on p-adic multiple L-functions. We consider ∞-adic and v-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 ∞-adic multiple zeta functions, (2) integral expression of v-adic multiple zeta functions themselves similar to those of p-adic multiple L-functions, (3) Kummer-type congruence for the special values of v-adic multiple zeta functions at integers (4) relationships between special values of ∞-adic and those of v-adic multipe zeta functions at negative integers and (5) orthognal properties of multiple zeta functions and multiple zeta star functions.

Related

• (p-adic) L-functions and (p-adic) (multiple) zeta values
• Desingularization of complex multiple zeta-functions, fundamentals of p-adic multiple L-functions, and evaluation of their special values
• Integrality of v-adic multiple zeta values
• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers