On qq-Analogs of Some Families of Multiple Harmonic Sum and Multiple Zeta Star Value Identities

In recent years, there has been intensive research on the ${\mathbb Q}$-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 $q\to 1$. The main result of the paper is 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 $\zeta^{\star}(s_1,\dots,s_r)$ with $s_i\in\{2,3\}$ span the vector space generated by multiple zeta values over ${\mathbb Q}$.Comment: The abstract and references are updated. Two new theorems, Theorem 1.4, Theorem 5.4, and Corollary 1.6 are adde

Generating functions for multiple zeta star values

We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value in terms of multiple alternating Euler sums, and specifically, reduce the length of blocks of twos in the resulting sums.Comment: To appear in Journal de Th\'eorie des Nombres de Bordeau