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

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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Multivariatep-Adic Fermionicq-Integral onℤpand Related Multiple Zeta-Type Functions

Abstract and Applied Analysis ◽

10.1155/2008/304539 ◽

2008 ◽

Vol 2008 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Min-Soo Kim ◽

Taekyun Kim ◽

Jin-Woo Son

Keyword(s):

Generating Functions ◽

Zeta Functions ◽

Bernoulli Polynomials ◽

Partial Answer ◽

Euler Polynomials ◽

Multiple Zeta

In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz's typeq-Bernoulli polynomials and obtained the distribution relation for them. They also raised the following problem:“are there analytic multiple twisted Carlitz's typeq-zeta functions which interpolate multiple twisted Carlitz's typeq-Euler (Bernoulli) polynomials?”The aim of this paper is to give a partial answer to this problem. Furthermore we derive some interesting identities related to twistedq-extension of Euler polynomials and multiple twisted Carlitz's typeq-Euler polynomials.

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

Glasgow Mathematical Journal ◽

10.1017/s0017089514000160 ◽

2014 ◽

Vol 57 (1) ◽

pp. 107-130 ◽

Cited By ~ 1

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.

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On the Functional Relations for the Euler-Zagier Multiple Zeta-functions

Tokyo Journal of Mathematics ◽

10.3836/tjm/1502179280 ◽

2018 ◽

Vol 41 (2) ◽

pp. 477-485

Author(s):

Soichi IKEDA ◽

Kaneaki MATSUOKA

Keyword(s):

Zeta Functions ◽

Functional Relations ◽

Multiple Zeta

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Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽

10.3390/sym12091431 ◽

2020 ◽

Vol 12 (9) ◽

pp. 1431

Author(s):

Junesang Choi ◽

Recep Şahin ◽

Oğuz Yağcı ◽

Dojin Kim

Keyword(s):

Zeta Function ◽

Generating Functions ◽

Recurrence Relations ◽

Zeta Functions ◽

Integral Representations ◽

Lerch Zeta Function ◽

Derivative Formulas ◽

The One ◽

Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

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