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Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values
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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.
Forward citations
Cited by 3 Pith papers
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Duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values
Two q-analogue duality formulas for Q-hat multiple zeta values are proved, yielding a previously unknown t-adic symmetric multiple zeta value duality.
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Ohno relation for regularized refined symmetric multiple zeta values
The authors generalize Takeyama's Ohno relation to regularized refined symmetric multiple zeta values, yielding a generating-function identity with gamma factors.
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On generic double shuffle relations, localized multiple polylogarithms and algebraic functions
A sketch of a construction of subvarieties of M_{0,n} carrying rational solutions to generic double shuffle equations, where the subvariety is defined as the locus where those equations hold.
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