p-adic multiple zeta values and binomial multiple harmonic sums

2025/11/28 by Hidekazu Furusho, Furusho, Hidekazu, David Jarossay +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2511.23255

Abstract

We present a concise method for deriving an explicit formula for p-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.

Citations

• p-adic hypergeometric function related with p-adic multiple polylogarithms
• Pro-unipotent harmonic actions and a computation of p-adic cyclotomic multiple zeta values
• Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values
• p-adic multiple zeta values II -- tannakian interpretations
• Groupes fondamentaux motiviques de Tate mixte

Related

• Non-vanishing of certain cyclotomic multiple harmonic sums and\n application to the non-vanishing of certain p-adic cyclotomic multiple zeta\n values
• A note on the algebra of p-adic multi-zeta values
• Pro-unipotent harmonic actions and a computation of p-adic cyclotomic multiple zeta values
• On harmonic sums and alternating Euler sums
• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation