On q-analogs of some families of multiple harmonic sums and multiple zeta star value identities

摘要

In recent years, there has been intensive research on the Q-linear relations between multiple zeta (star) values. In this paper, we prove many families of identities involving the q-analog of these values, from which we can always recover the corresponding classical identities by taking q -> 1. The main results of the paper (Theorems 1.4 and 5.4) are the duality relations between multiple zeta star values and Euler sums and their q-analogs, which are generalizations of the Two-one formula and some multiple harmonic sum identities and their q-analogs proved by the authors recently. Such duality relations lead to a proof of the conjecture by Ihara et al. that the Hoffman star-elements. zeta(star)(s(1),..., s(r)) with s(i) is an element of {2, 3} span the vector space generated by multiple zeta values over Q.