scholarly journals Hoffman’s conjectural identity

2019 ◽  
Vol 15 (01) ◽  
pp. 167-171 ◽  
Author(s):  
Minoru Hirose ◽  
Nobuo Sato
Keyword(s):  
Multiple Zeta Values ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Special Case

In this paper, we prove a family of identities among multiple zeta values, which contains as a special case a conjectural identity of Hoffman. We use the iterated integrals on [Formula: see text] for our proof.

Several weighted sum formulas of multiple zeta values

2017 ◽  
Vol 13 (09) ◽  
pp. 2253-2264 ◽  
Author(s):  
Minking Eie ◽  
Wen-Chin Liaw ◽  
Yao Lin Ong
Keyword(s):  
Real Number ◽  
Weighted Sum ◽  
Multiple Zeta Values ◽  
Explicit Evaluation ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Number Formula ◽  
Positive Integers ◽  
Special Case

For a real number [Formula: see text] and positive integers [Formula: see text] and [Formula: see text] with [Formula: see text], we evaluate the sum of multiple zeta values [Formula: see text] explicitly in terms of [Formula: see text] and [Formula: see text]. The special case [Formula: see text] gives an evaluation of [Formula: see text]. An explicit evaluation of the multiple zeta-star value [Formula: see text] is also obtained, as well as some applications to evaluation of multiple zeta values with even arguments.

scholarly journals Iterated integrals on products of one variable multiple polylogarithms

2020 ◽  
Vol 16 (10) ◽  
pp. 2167-2186
Author(s):  
Jiangtao Li
Keyword(s):  
Multiple Zeta Values ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Multiple Polylogarithms ◽  
Series Representations ◽  
Zeta Values

In this paper, we show that the iterated integrals on products of one variable multiple polylogarithms from [Formula: see text] to [Formula: see text] are actually in the algebra of multiple zeta values if they are convergent. In the divergent case, we define the regularized iterated integrals from [Formula: see text] to [Formula: see text]. By the same method, we show that the regularized iterated integrals are also in the algebra of multiple zeta values. As an application, we give new series representations for multiple zeta values and calculate some interesting examples of iterated integrals.

scholarly journals Duality/sum formulas for iterated integrals and their application to multiple zeta values

2019 ◽  
Vol 195 ◽  
pp. 72-83 ◽  
Author(s):  
Minoru Hirose ◽  
Kohei Iwaki ◽  
Nobuo Sato ◽  
Koji Tasaka
Keyword(s):  
Multiple Zeta Values ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values

SOME IDENTITIES IN THE HARMONIC ALGEBRA CONCERNED WITH MULTIPLE ZETA VALUES

2013 ◽  
Vol 09 (03) ◽  
pp. 783-798 ◽  
Author(s):  
ZHONG-HUA LI
Keyword(s):  
Polynomial Algebra ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Special Case

Let 𝔄 be a commutative ℚ-algebra, A be an alphabet of non-commutative letters and 𝔥1 be the non-commutative polynomial algebra generated by the set A over the algebra 𝔄. The harmonic algebra 𝔥1 is closely related to multiple zeta values and multiple zeta-star values in some special case. Some identities in the algebra 𝔥1 are given.

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.

scholarly journals Multiple Dedekind zeta functions

2017 ◽  
Vol 2017 (722) ◽  
Author(s):  
Ivan Emilov Horozov
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Quadratic Fields ◽  
Multiple Zeta Values ◽  
Imaginary Quadratic Fields ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values ◽  
New Type

AbstractIn this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler’s multiple zeta values. Over imaginary quadratic fields MDZV capture, in particular, multiple Eisenstein series [

scholarly journals A new proof of the duality of multiple zeta values and its generalizations

2019 ◽  
Vol 15 (06) ◽  
pp. 1261-1265
Author(s):  
Shin-ichiro Seki ◽  
Shuji Yamamoto
Keyword(s):  
Multiple Zeta Values ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values

We give a new proof of the duality of multiple zeta values, which makes no use of the iterated integrals. The same method is also applicable to Ohno’s relation for ([Formula: see text]-)multiple zeta values.

Motivic multiple zeta values relative to μ2

2020 ◽  
Vol 14 (10) ◽  
pp. 2685-2712
Author(s):  
Zhongyu Jin ◽  
Jiangtao Li
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values
Sign in / Sign up

Export Citation Format

Share Document