Variants of Multiple Zeta Values of Level Two and Four

报告题目: Variants of Multiple Zeta Values of Level Two and Four




报告摘要:In this talk, we introduce various variants of multiple zeta values (MZVs) of level two and four. For example, the multiple mixed values (MMVs) and the alternating multiple mixed values (AMMVs), which forms are subspaces of the space of colored MZVs of level two and four, respectively. These variants include both Hoffman's (alternating) multiple t-values and Kaneko-Tsumura's (alternating) multiple T-values as special cases. We will explore their properties similar to ordinary MZVs such as the duality, integral shuffle and series stuffle relations. In the end, we discuss the dimensions of a few interesting subspaces of AMMVs for weight less than 9 and provide some conjectures. This work is joint with L. Yan and J. Zhao.