On Witten multiple zeta-functions associated with semisimple Lie algebras II
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- Komori Yasushi KOMORI Yasushi
- Graduate School of Mathematics Nagoya University
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- Matsumoto Kohji MATSUMOTO Kohji
- Graduate School of Mathematics Nagoya University
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- Tsumura Hirofumi TSUMURA Hirofumi
- Department of Mathematics and Information Sciences Tokyo Metropolitan University
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Author(s)
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- Komori Yasushi KOMORI Yasushi
- Graduate School of Mathematics Nagoya University
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- Matsumoto Kohji MATSUMOTO Kohji
- Graduate School of Mathematics Nagoya University
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- Tsumura Hirofumi TSUMURA Hirofumi
- Department of Mathematics and Information Sciences Tokyo Metropolitan University
Abstract
This is a continuation of our previous result, in which properties of multiple zeta-functions associated with simple Lie algebras of <i>A</i><sub><i>r</i></sub> 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 <i>B</i><sub><i>r</i></sub>, <i>C</i><sub><i>r</i></sub>, and <i>D</i><sub><i>r</i></sub> types.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 62(2), 355-394, 2010-04-01
The Mathematical Society of Japan
References: 22
-
1
- Analytic continuation of multiple zeta-functions and their values at non-positive integers
-
AKIYAMA S.
Acta Arith 98, 107-116, 2001
Cited by (1)
-
2
- <no title>
-
BOURBAKI N.
Groupes et Algebres de Lie Chapitres 4,5 et 6, 1968
Cited by (1)
-
3
- Singularites des series de Dirichlet associees a des polynomes de plusieurs variables et applications a la theorie analytique des nombres
-
ESSOUABRI D.
These, Univ. Henri Poincare-Nancy I, 1995
Cited by (1)
-
4
- Singularites des series de Dirichlet associees a des polynomes de plusieurs variables et applications en theorie analytique des nombres
-
ESSOUABRI D.
Ann. Inst. Fourier 47, 429-483, 1997
Cited by (1)
-
5
- Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions
-
GUNNELLS P. E.
Duke Math. J. 118, 229-260, 2003
Cited by (1)
-
6
- <no title>
-
HUMPHREYS J. E.
Introduction to Lie Algebras and Representation Theory, 1972
Cited by (1)
-
7
- Zeta-functions of root systems
-
KOMORI Y.
The Conference on L-functions, Fukuoka, 2006, 115-140, 2007
Cited by (1)
-
8
- Functional relations for zeta-functions of root systems
-
KOMORI Y.
Number Theory : Dreaming in Dreams-Proceedings of the 5th China-Japan Seminar, 2010, 135-183, 2010
Cited by (1)
-
9
- On Witten multiple zeta-functions associated with semisimple Lie algebras III
-
KOMORI Y.
arXiv:0907.0955
Cited by (1)
-
10
- On the analytic continuation of various multiple zeta-functions
-
MATSUMOTO K.
Number Theory for the Millennium II, 417-440, 2002
Cited by (1)
-
11
- Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
-
MATSUMOTO K.
Nagoya Math. J. 172, 59-102, 2003
Cited by (1)
-
12
- On Mordell-Tornheim and other multiple zeta-functions
-
MATSUMOTO K.
Proc. Session in Analytic Number Theory and Diophantine Equations, Bonn, 2003, 2003
Cited by (1)
-
13
- On Witten multiple zeta-functions associated with semisimple Lie algebras I
-
MATSUMOTO K.
Ann. Inst. Fourier 56, 1457-1504, 2006
Cited by (1)
-
14
- <no title>
-
SAMELSON H.
Notes on Lie Algebras, 1990
Cited by (1)
-
15
- Harmonic double series
-
TORNHEIM L.
Amer. J. Math. 72, 303-314, 1950
Cited by (1)
-
16
- On quantum gauge theories in two dimensions
-
WITTEN E.
Commun. Math. Phys. 141, 153-209, 1991
Cited by (1)
-
17
- Values of zeta functions and their applications
-
ZAGIER D.
First European Congress of Mathematics, 1994 II, 497-512, 1994
Cited by (1)
-
18
- Zeta and L-functions and Bernoulli polynomials of root systems
-
Komori Yasushi , Matsumoto Kohji , Tsumura Hirofumi
Proceedings of the Japan Academy Ser. A Mathematical Sciences 84(5), 57-62, 2008-05
IR Cited by (1)
-
19
- The Analytic Continuation and the Asymptotic Behaviour of Certain Multiple Zeta-Functions(III)
-
MATSUMOTO K.
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi 54(2), 163-186, 2005-12
-
20
- The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions I
-
MATSUMOTO K.
J. Number Theory 101, 223-243, 2003
DOI Cited by (2)
-
21
- On the evaluation of some multiple series
-
MORDELL L. J.
J. London Math. Soc. 33, 368-371, 1958
DOI Cited by (2)
-
22
- On Witten's type of zeta values attached to SO(5)
-
TSUMURA H.
Arch. Math. 82, 147-152, 2004
DOI Cited by (2)