On Witten multiple zeta-functions associated with semisimple Lie algebras II

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概要

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• This is a continuation of our previous result, in which properties of multiple zeta-functions associated with simple Lie algebras of Ar type have been studied. In the present paper we consider more general situation, and discuss the Lie theoretic background structure of our theory. We show a recursive structure in the family of zeta-functions of sets of roots, which can be explained by the order relation among roots. We also point out that the recursive structure can be described in terms of Dynkin diagrams. Then we prove several analytic properties of zeta-functions associated with simple Lie algebras of Br, Cr, and Dr types.

著者

• MATSUMOTO Kohji

  Graduate School of Mathematics, Nagoya University

• Komori Yasushi

  Graduate School of Mathematics, Nagoya University

• Tsumura Hirofumi

  Department of Mathematics and Information Sciences, Tokyo Metropolitan University

関連論文

• On $L$-functions over function fields : Power-means of error-terms and distribution of $L^\prime/L$-values (Algebraic Number Theory and Related Topics 2008)
• On Witten multiple zeta-functions associated with semisimple Lie algebras II
• The joint universality and the functional independence for Lerch zeta-functions
• ON THE SIEGEL-TATUZAWA THEOREM FOR A CLASS OF L-FUNCTIONS
• On Witten multiple zeta-functions associated with semisimple Lie algebras II

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