ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV
説明
<jats:title>Abstract</jats:title><jats:p>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 <jats:italic>A</jats:italic><jats:sub>2</jats:sub>, <jats:italic>A</jats:italic><jats:sub>3</jats:sub>, <jats:italic>B</jats:italic><jats:sub>2</jats:sub>, <jats:italic>B</jats:italic><jats:sub>3</jats:sub> and <jats:italic>C</jats:italic><jats:sub>3</jats:sub>. In this paper, we consider the case of <jats:italic>G</jats:italic><jats:sub>2</jats:sub>-type. We define certain analogues of Bernoulli polynomials of <jats:italic>G</jats:italic><jats:sub>2</jats:sub>-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of <jats:italic>G</jats:italic><jats:sub>2</jats:sub>-type. Next, we consider the meromorphic continuation of the zeta-function of <jats:italic>G</jats:italic><jats:sub>2</jats:sub>-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.</jats:p>
収録刊行物
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- Glasgow Mathematical Journal
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Glasgow Mathematical Journal 53 (1), 185-206, 2010-08-25
Cambridge University Press (CUP)
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詳細情報 詳細情報について
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- CRID
- 1360285707998907264
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- ISSN
- 1469509X
- 00170895
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