Proceedings of the Japan Academy, Series A, Mathematical Sciences

Multiple zeta values and zeta-functions of root systems

Yasushi Komori, Kohji Matsumoto, and Hirofumi Tsumura

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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: 1 June 2011

Permanent link to this document
http://projecteuclid.org/euclid.pja/1306934067

Digital Object Identifier
doi:10.3792/pjaa.87.103

Zentralblatt MATH identifier
05944199

Mathematical Reviews number (MathSciNet)
MR2803890

Subjects
Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Secondary: 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)

Keywords
Multiple zeta-values root systems witten zeta-functions

Citation

Komori, Yasushi; Matsumoto, Kohji; Tsumura, Hirofumi. Multiple zeta values and zeta-functions of root systems. Proceedings of the Japan Academy, Series A, Mathematical Sciences 87 (2011), no. 6, 103--107. doi:10.3792/pjaa.87.103. http://projecteuclid.org/euclid.pja/1306934067.


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