Depth reductions for associators

Abstract

We prove that for any associator, two specific families of coefficients of the associator can be expressed in terms of coefficients of lower depth. Combining these results to our notions of adjoint $p$-adic multiple zeta values and multiple harmonic values, we obtain a new point of view on the question of relating $p$-adic and finite multiple zeta values, and a few other application to the study of $p$-adic multiple zeta values via explicit formulas.

19 pages

References in corpus (7)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
• Multiple Modular Values and the relative completion of the fundamental group of $M_{1,1}$
• The parity theorem for multiple polylogarithms
• Finite real multiple zeta values generate the whole space $Z$
• Adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values
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• Pro-unipotent harmonic actions and a computation of $p$-adic cyclotomic multiple zeta values

Cited by in corpus (4)

• The parity theorem for multiple polylogarithms
• A bound on the norm of overconvergent $p$-adic multiple polylogarithms
• Pro-unipotent harmonic actions and a computation of $p$-adic cyclotomic multiple zeta values
• Truncated $t$-adic symmetric multiple zeta values and double shuffle relations