## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Multiple zeta values and zeta-functions of root systems

#### Abstract

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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 87, Number 6 (2011), 103-107.

Dates
First available in Project Euclid: 1 June 2011

http://projecteuclid.org/euclid.pja/1306934067

Digital Object Identifier
doi:10.3792/pjaa.87.103

Mathematical Reviews number (MathSciNet)
MR2803890

Zentralblatt MATH identifier
1256.11048

#### Citation

Komori, Yasushi; Matsumoto, Kohji; Tsumura, Hirofumi. Multiple zeta values and zeta-functions of root systems. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 6, 103--107. doi:10.3792/pjaa.87.103. http://projecteuclid.org/euclid.pja/1306934067.

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