Part VI. An introduction to the theory of zeta-functions of root systems

2010 ◽  
pp. 115-140 ◽  
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Root Systems

scholarly journals Zeta Functions of Root Systems

2006 ◽  
pp. 115-140 ◽  
Author(s):  
Y. KOMORI ◽  
K. MATSUMOTO ◽  
H. TSUMURA
Keyword(s):  
Zeta Functions ◽  
Root Systems

scholarly journals Zeta-functions of root systems and Poincaré polynomials of Weyl groups

2020 ◽  
Vol 72 (1) ◽  
pp. 87-126
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Root Systems ◽  
Weyl Groups

FUNCTIONAL RELATIONS FOR ZETA-FUNCTIONS OF ROOT SYSTEMS

Number Theory ◽  
2009 ◽  
Author(s):  
YASUSHI KOMORI ◽  
KOHJI MATSUMOTO ◽  
HIROFUMI TSUMURA
Keyword(s):  
Zeta Functions ◽  
Root Systems ◽  
Functional Relations

scholarly journals Multiple zeta values and zeta-functions of root systems

2011 ◽  
Vol 87 (6) ◽  
pp. 103-107 ◽  
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Root Systems ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

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

2010 ◽  
Vol 53 (1) ◽  
pp. 185-206 ◽  
Author(s):  
YASUSHI KOMORI ◽  
KOHJI MATSUMOTO ◽  
HIROFUMI TSUMURA
Keyword(s):  
Zeta Function ◽  
Lie Algebras ◽  
Generating Functions ◽  
Zeta Functions ◽  
Bernoulli Polynomials ◽  
Root Systems ◽  
Previous Method ◽  
Meromorphic Continuation ◽  
Functional Relations ◽  
Multiple Zeta

AbstractIn 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.

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