scholarly journals On a generalization of the cyclic sum formula for finite multiple zeta and zeta-star values

2020 ◽  
Vol 31 (6) ◽  
pp. 1144-1154
Author(s):  
Hideki Murahara
Keyword(s):  
Multiple Zeta ◽  
Sum Formula

scholarly journals ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

2015 ◽  
Vol 93 (2) ◽  
pp. 186-193 ◽  
Author(s):  
MASANOBU KANEKO ◽  
MIKA SAKATA
Keyword(s):  
Explicit Formula ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values ◽  
Sum Formula

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

scholarly journals Sum formula for finite multiple zeta values

2015 ◽  
Vol 67 (3) ◽  
pp. 1069-1076 ◽  
Author(s):  
Shingo SAITO ◽  
Noriko WAKABAYASHI
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Sum Formula

ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES AND FINITE MULTIPLE ZETA VALUES

2019 ◽  
Vol 101 (1) ◽  
pp. 23-34
Author(s):  
HIDEKI MURAHARA ◽  
TAKUYA MURAKAMI
Keyword(s):  
Linear Relation ◽  
Analogous Result ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Natural Generalisation ◽  
Sum Formula

We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.

Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula

2011 ◽  
Vol 63 (2) ◽  
pp. 241-276 ◽  
Author(s):  
Driss Essouabri ◽  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Zeta Functions ◽  
Linear Recurrence ◽  
Multiple Zeta ◽  
Sum Formula ◽  
Recurrence Sequences ◽  
Holomorphic Continuation

Abstract We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions fromwhich some generalizations of the classical sum formula can be deduced.

scholarly journals WEIGHTED SUMS WITH TWO PARAMETERS OF MULTIPLE ZETA VALUES AND THEIR FORMULAS

2012 ◽  
Vol 08 (08) ◽  
pp. 1903-1921 ◽  
Author(s):  
TOMOYA MACHIDE
Keyword(s):  
Weighted Sums ◽  
Multiple Zeta Values ◽  
Linear Combinations ◽  
Fixed Weight ◽  
Rational Polynomial ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Sum Formula ◽  
Riemann Zeta ◽  
Two Parameters

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum formula, have been studied by many people. In this paper, we give two formulas of weighted sums with two parameters of multiple zeta values. As applications of the formulas, we find some linear combinations of multiple zeta values which can be expressed as polynomials of usual zeta values with coefficients in the rational polynomial ring generated by the two parameters, and obtain some identities for weighted sums of multiple zeta values.

scholarly journals Zeta Value Identities From Iterated Integrals With Additional Factors

2019 ◽  
Vol 11 (5) ◽  
pp. 40
Author(s):  
Chan-Liang Chung ◽  
Minking Eie
Keyword(s):  
Integral Representation ◽  
Linear Combination ◽  
Multiple Zeta Values ◽  
Iterated Integrals ◽  
Multiple Zeta Value ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Sum Formula

A multiple zeta value can always be represented by its Drinfel’d integral. If we add some factors appeared in the integrand of the integral representation of the multiple zeta value, it would still represent a linear combination of multiple zeta values, but the depths and weights may decrease. In this paper, we shall investigate some of multiple zeta values obtained from Drinfel’d integral with additional factors aforementioned and study a class of deformation of multiple zeta values. Results are then obtained as analogues or generalizations of the sum formula of multiple zeta values.

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