Multiple zeta values and zeta-functions of root systems

作者：Komori Yasushi^*; Matsumoto Kohji; Tsumura Hirofumi

来源：Proceedings of the Japan Academy Series A-Mathematical Sciences, 2011, 87(6): 103-107.

DOI：10.3792/pjaa.87.103

• Multiple zeta-values
• root systems
• witten zeta-functions

We propose the viewpoint that the r-ple zeta-function of Euler-Zagier type can be regarded as a specialization of the zeta-function associated with the root system of C-r type. From this viewpoint, we can see that Zagier's well-known formula for multiple zeta values (MZVs) coincides with Witten's volume formula associated with a sub-root system of C-r type. Based on this observation, we generalize Zagier's formula and also give analogous results which correspond to a sub-root system of B-r type. We announce those results as well as some relevant results for partial multiple zeta values.

• 出版日期2011-6