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

Abstract

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

20 pages. Part III-3 of "$p$-adic cyclotomic multiple zeta values and $p$-adic pro-unipotent harmonic actions"

References in corpus (2)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• On The Prime Numbers In Intervals

Cited by in corpus (1)

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