scholarly journals On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III

2012 ◽  
pp. 223-286 ◽  
Author(s):  
Yasushi Komori ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Lie Algebras ◽  
Zeta Functions ◽  
Semisimple Lie Algebras ◽  
Multiple Zeta

scholarly journals On Witten multiple zeta-functions associated with semisimple Lie algebras II

2010 ◽  
Vol 62 (2) ◽  
pp. 355-394 ◽  
Author(s):  
Yasushi KOMORI ◽  
Kohji MATSUMOTO ◽  
Hirofumi TSUMURA
Keyword(s):  
Lie Algebras ◽  
Zeta Functions ◽  
Semisimple Lie Algebras ◽  
Multiple Zeta

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

2014 ◽  
Vol 57 (1) ◽  
pp. 107-130 ◽  
Author(s):  
YASUSHI KOMORI ◽  
KOHJI MATSUMOTO ◽  
HIROFUMI TSUMURA
Keyword(s):  
Positive Integer ◽  
Zeta Function ◽  
Root System ◽  
Lie Algebras ◽  
Zeta Functions ◽  
Simple Lie Algebras ◽  
Integer Points ◽  
Multiple Zeta

AbstractWe study the values of the zeta-function of the root system of type G2 at positive integer points. In our previous work we considered the case when all integers are even, but in the present paper we prove several theorems which include the situation when some of the integers are odd. The underlying reason why we may treat such cases, including odd integers, is also discussed.

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.

Semisimple Lie Algebras of Operators

2001 ◽  
pp. 181-202
Author(s):  
Daniel Beltiţă ◽  
Mihai Şabac
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras

Periods, Multiple Zeta Functions and ζ(3)

2014 ◽  
pp. 185-203
Author(s):  
M. Ram Murty ◽  
Purusottam Rath
Keyword(s):  
Zeta Functions ◽  
Multiple Zeta

Semisimple Lie Algebras

2020 ◽  
pp. 71-134
Author(s):  
Morikuni Goto ◽  
Frank D. Grosshans
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras
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