Derivations on the algebra of multiple harmonic q-series and their applications

Abstract

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a byproduct we obtain Ohno-type relations for finite multiple harmonic q-series at a root of unity. This is a pre-print of an article published in The Ramanujan Journal. The final authenticated version is available online at: https://doi.

Finite and symmetric colored multiple zeta values and multiple harmonic q-series at roots of unity

“…In a similar manner to [2], one can As a corollary, we see that a relation among z m (k; ζ m )'s, whose coefficients are in Q and do not depend on the choices of ζ m , gives rise to a relation among finite and symmetric multiple zeta values in the same form. So, one can derive partial evidence of the Kaneko-Zagier conjecture from the study of relations of z m (k; ζ m )'s (see [2,3,13]).…”