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

By Y. Komori, Kohji Matsumoto, Hirofumi Tsumura. Glasgow Mathematical Journal, 2009

71 citations recorded by the source corpus.

Abstract 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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/ba0ffeba8fe8e9b5609f8381a78eafc65bcea309