On a variant of 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.

On a weighted sum of multiple T-values of fixed weight and depth

“…which is a special case of the duality of the multiple T -values proved in [4], and the inequality T (n + 1) ≤ 2, we obtain…”

“…due to Kaneko and Tsumura [4,Theorem 3.2]. See [1] and the references therein for recent results on weighted sum of variants of multiple zeta values.…”

Two Variants of Euler Sums

“…Moreover, we can use the quadratic sum S p 1 p 2 ,q to evaluate the triple Kaneko-Tsumura T -values with weight even. The Kaneko-Tsumura T -zeta values are defined by [19,20]…”

Weighted sum formula of multiple $L$-values and its applications

“…In [6], Xu and Zhao studied a variant of multiple zeta values of level 2 (which is called multiple mixed values therein), which forms a subspace of the space of alternating multiple zeta values. This variant includes both Hoffman's multiple t-values [3] and Kaneko-Tsumura's multiple T -values [4] as special cases. The multiple zeta values of any level is introduced by Yuan and Zhao in [7].…”

“…As applications, we provide some sum formulas and weighted sum formulas of double zeta values of level 2 and level 3. In particular, we reprove the weighted sum formula of double T -values appeared in [4].…”