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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
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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

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