Depth reductions for associators

preprint2020arXivOpen access

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 pp-adic multiple zeta values and multiple harmonic values, we obtain a new point of view on the question of relating pp-adic and finite multiple zeta values, and a few other application to the study of pp-adic multiple zeta values via explicit formulas.

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