Pro-unipotent harmonic actions and a computation of p-adic cyclotomic multiple zeta values

2015/01/20 by David Jarossay, Jarossay, David · 5 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1501.04893

openalex publication_date 2015/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain formulas relating p-adic cyclotomic multiple zeta values and cyclotomic multiple harmonic sums. In particular, we obtain a series formula for p-adic cyclotomic multiple zeta values, and conversely a formula for certain cyclotomic multiple harmonic sums in terms of p-adic cyclotomic multiple zeta values. Our formulas are related to the motivic framework via a new notion which we call pro-unipotent harmonic actions, which are ad hoc p-adic byproducts of the Ihara action. As an application, we prove a conjecture of Akagi, Hirose and Yasuda on the relation between p-adic multiple zeta values and multiple harmonic sums, and we generalize it to the cyclotomic case. We also deduce bounds on the dimension of the spaces of finite cyclotomic multiple zeta values.

Citations

• Multiple polylogarithms and mixed Tate motives

Cited by

• p-adic multiple zeta values and binomial multiple harmonic sums
• A Lie algebra associated with adjoint multiple zeta values
• Non-vanishing of certain cyclotomic multiple harmonic sums and\n application to the non-vanishing of certain p-adic cyclotomic multiple zeta\n values
• p-adic multiple zeta values and p-adic pro-unipotent harmonic\n actions : summary of parts I and II
• Integrality of v-adic multiple zeta values

Related

• p-adic multiple zeta values and p-adic pro-unipotent harmonic\n actions : summary of parts I and II
• An explicit theory of π₁^\un,\crys(ℙ¹ - \0,μ_N,∞\) - II-2 : From standard algebraic relations of weighted multiple harmonic sums to those of cyclotomic p-adic multiple zeta values
• Non-vanishing of certain cyclotomic multiple harmonic sums and\n application to the non-vanishing of certain p-adic cyclotomic multiple zeta\n values
• Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values
• p-adic multiple zeta values at roots of unity and p-adic pro-unipotent harmonic actions - IV-1 : p-adic multiple zeta values at roots of unity extended to sequences of integers of any sign