Speaker: 徐策，安徽师范大学

Inviter: 陈绍示（中国科学院数学机械化重点实验室）

Title: Explicit Relations of Some Variants of Convoluted Multiple Zeta Values

Language: Chinese

Time & Venue: 2025.05.23 16:00-17:00 思源楼525

Abstract: Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values (MVZs) around 2016. In this talk, we will first introduce some explicit formulas involving these values and their alternating version by using iterated integrals, which enable us to derive some explicit relations of the multiple polylogarithm (MPL) functions. Next, we define convoluted multiple t-values and multiple mixed values (MMVs) as level two analogs of convoluted MZVs, and, similar to convoluted MZVs, use iterated integrals to find some relations of these level two analogs. We will then consider the parametric MPLs and the parametric multiple harmonic (star) sums, and extend the Kaneko-Yamamoto’s “integral-series” identity of MZVs to MPLs and MMVs. Finally, we will study multiple integrals of MPLs and MMVs by generalizing Yamamoto’s graphical representations to multiple-labeled posets. This is a joint work with Jianqiang Zhao.