Room 638, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 638室)

Sum Formulas of Multiple Zeta Values with Arguments are Multiple of a Positive Integer

Chan-Liang Chung (Academia Sinica)

Abstract

Let be a multiple zeta value of depth and weight . Several explicit values of multiple zeta values are interesting and known for special index sets. A principle goal in the theoretical study of multiple zeta values is to determine all possible algebraic relations among them. For , let be the sum of all multiple zeta values of depth and weight with arguments are multiple of . In this talk, an identity which is closely related to the sum relation involving multiple zeta values with even arguments will be presented. Also, I will build up some variations of multiple zeta values and investigate their relations. In particular, I will give a simple proof of the well-known sum formula of multiple zeta values and derive some generalizations.

This is joint work with K.-W. Chen and M. Eie.