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ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV

Published online by Cambridge University Press:  25 August 2010

YASUSHI KOMORI ,
KOHJI MATSUMOTO  and
HIROFUMI TSUMURA
YASUSHI KOMORI
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan e-mail: komori@math.nagoya-u.ac.jp, kohjimat@math.nagoya-u.ac.jp
KOHJI MATSUMOTO
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan e-mail: komori@math.nagoya-u.ac.jp, kohjimat@math.nagoya-u.ac.jp
HIROFUMI TSUMURA
Affiliation:
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan e-mail: tsumura@tmu.ac.jp
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Abstract

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In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types A2, A3, B2, B3 and C3. In this paper, we consider the case of G2-type. We define certain analogues of Bernoulli polynomials of G2-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of G2-type. Next, we consider the meromorphic continuation of the zeta-function of G2-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.

Keywords

Primary 11M41Secondary 17B2040B05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 185 - 206
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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