Geodesic
ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV
Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 185-206

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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.
DOI : 10.1017/S0017089510000613
Mots-clés : Primary 11M41, Secondary 17B20, 40B05 
KOMORI, YASUSHI; MATSUMOTO, KOHJI; TSUMURA, HIROFUMI. ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV. Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 185-206. doi: 10.1017/S0017089510000613
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     title = {ON {WITTEN} {MULTIPLE} {ZETA-FUNCTIONS} {ASSOCIATED} {WITH} {SEMI-SIMPLE} {LIE} {ALGEBRAS} {IV}},
     journal = {Glasgow mathematical journal},
     pages = {185--206},
     year = {2011},
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     number = {1},
     doi = {10.1017/S0017089510000613},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000613/}
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