Non-vanishing of certain cyclotomic multiple harmonic sums and\n application to the non-vanishing of certain p-adic cyclotomic multiple zeta\n values

2017/07/06 by David Jarossay, Jarossay, David
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1707.01924

openalex publication_date 2017/07/06 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

We define and apply a method to study the non-vanishing of p-adic\ncyclotomic multiple zeta values. We prove the non-vanishing of certain\ncyclotomic multiple harmonic sums, and, via a formula proved in another paper,\nwhich expresses a cyclotomic multiple harmonic sums as an infinite sum of\nproducts of p-adic cyclotomic multiple zeta values, this implies the\nnon-vanishing of certain p-adic cyclotomic multiple zeta values.\n

Citations

• Multiple polylogarithms and mixed Tate motives
• Pro-unipotent harmonic actions and a computation of p-adic cyclotomic multiple zeta values
• Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values

Cited by

• p-adic multiple zeta values and p-adic pro-unipotent harmonic\n actions : summary of parts I and II

Related

• Pro-unipotent harmonic actions and a computation of p-adic cyclotomic multiple zeta values
• p-adic multiple zeta values and binomial multiple harmonic sums
• Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values
• Cyclotomic p-adic multi-zeta values
• 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