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On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III

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Part of the book series: Progress in Mathematics ((PM,volume 300))

Abstract

We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of these functional relations is given by the symmetry with respect to Weyl groups. From these relations, we can deduce explicit expressions of values of Witten zeta-functions at positive even integers, which are written in terms of generalized Bernoulli numbers of root systems. Furthermore, we introduce generating functions of Bernoulli numbers of root systems, using which we can give an algorithm of calculating Bernoulli numbers of root systems.

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Acknowledgements

The authors express their sincere gratitude to the organizers and the editors who gave the occasion of a talk at the conference and the publication of a paper in the present proceedings. The authors are also indebted to the referee for useful comments and suggestions.

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Correspondence to Kohji Matsumoto .

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Komori, Y., Matsumoto, K., Tsumura, H. (2012). On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III. In: Bump, D., Friedberg, S., Goldfeld, D. (eds) Multiple Dirichlet Series, L-functions and Automorphic Forms. Progress in Mathematics, vol 300. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8334-4_11

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