Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values

Abstract

We introduce adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values. They are two variants of cyclotomic multiple zeta values, closely related to each other. They arise as key tools for the study of $p$-adic cyclotomic multiple zeta values. Moreover, cyclotomic multiple harmonic values provide an adelic lift to a cyclotomic generalization of finite multiple zeta values. We establish certain standard properties of these two objects. We consider two types of properties : some related to double shuffle relations, and some related to associator and Kashiwara-Vergne relations.

37 pages. Part II-1 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
• Finite real multiple zeta values generate the whole space $Z$

Cited by in corpus (8)

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• Depth reductions for associators
• On variants of symmetric multiple zeta-star values and the cyclic sum formula
• Truncated $t$-adic symmetric multiple zeta values and double shuffle relations
• Non-vanishing of certain cyclotomic multiple harmonic sums and application to the non-vanishing of certain $p$-adic cyclotomic multiple zeta values
• Supercongruences of multiple harmonic $q$-sums and generalized finite/symmetric multiple zeta values
• Finite and symmetric colored multiple zeta values and multiple harmonic q-series at roots of unity
• A note on ${\mathcal{F}}_n$-multiple zeta values