On multiple zeta values of level two

Abstract

We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the ‘shuffle counterpart’ of Hoffman’s ‘odd variant’, exhibits nice properties such as duality, shuffle product, parity results, etc., like ordinary multiple zeta values. We also give some conjectures on relations between our values, Hoffman’s values, and multiple zeta values.