Open Access
June 2011 Multiple zeta values and zeta-functions of root systems
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
Proc. Japan Acad. Ser. A Math. Sci. 87(6): 103-107 (June 2011). DOI: 10.3792/pjaa.87.103


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.


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Yasushi Komori. Kohji Matsumoto. Hirofumi Tsumura. "Multiple zeta values and zeta-functions of root systems." Proc. Japan Acad. Ser. A Math. Sci. 87 (6) 103 - 107, June 2011.


Published: June 2011
First available in Project Euclid: 1 June 2011

zbMATH: 1256.11048
MathSciNet: MR2803890
Digital Object Identifier: 10.3792/pjaa.87.103

Primary: 11M41
Secondary: 40B05

Keywords: Multiple zeta-values , Root systems , Witten zeta-functions

Rights: Copyright © 2011 The Japan Academy

Vol.87 • No. 6 • June 2011
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