Integrality of v-adic multiple zeta values

2020/01/07 by Yen-Tsung Chen, Chen, Yen-Tsung
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.01855

openalex publication_date 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove the integrality of v-adic multiple zeta values (MZVs). For any index \mathfraks∈ℕ^r and finite place v∈ A:=\mathbbF_q[θ], Chang and Mishiba introduced the notion of the v-adic MZVs ζ_A(\mathfraks)_v, which is a function field analogue of Furusho's p-adic MZVs. By estimating the v-adic valuation of ζ_A(\mathfraks)_v, we show that ζ_A(\mathfraks)_v is a v-adic integer for almost all v. This result can be viewed as a function field analogue of the integrality of p-adic MZVs, which was proved by Akagi-Hirose-Yasuda and Chatzistamatiou.

Citations

• Periods and mixed motives
• Pro-unipotent harmonic actions and a computation of p-adic cyclotomic multiple zeta values

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