Explicit Formulas of Some Mixed Euler Sums via Alternating Multiple Zeta Values

2020 ◽  
Vol 43 (5) ◽  
pp. 3809-3827
Author(s):  
Ce Xu
Keyword(s):  
Multiple Zeta Values ◽  
Explicit Formulas ◽  
Euler Sums ◽  
Multiple Zeta ◽  
Zeta Values

Zeta Mahler measures, multiple zeta values and L-values

2015 ◽  
Vol 11 (07) ◽  
pp. 2239-2246
Author(s):  
Yoshitaka Sasaki
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Mahler Measure ◽  
Multiple Zeta Values ◽  
Explicit Formulas ◽  
Multiple Zeta ◽  
Zeta Values

The zeta Mahler measure is the generating function of higher Mahler measures. In this article, explicit formulas of higher Mahler measures, and relations between higher Mahler measures and multiple zeta (star) values are showed by observing connections between zeta Mahler measures and the generating functions of multiple zeta (star) values. Additionally, connections between higher Mahler measures and Dirichlet L-values associated with primitive quadratic characters are discussed.

Generalized harmonic numbers and Euler sums

2017 ◽  
Vol 13 (02) ◽  
pp. 513-528 ◽  
Author(s):  
Kwang-Wu Chen
Keyword(s):  
Zeta Functions ◽  
Multiple Zeta Values ◽  
Harmonic Numbers ◽  
Special Values ◽  
Euler Sums ◽  
Summation Formulas ◽  
Multiple Zeta ◽  
Zeta Values ◽  
New Formula ◽  
Generalized Harmonic Numbers

In this paper, we investigate two kinds of Euler sums that involve the generalized harmonic numbers with arbitrary depth. These sums establish numerous summation formulas including the special values of Arakawa–Kaneno zeta functions and a new formula of multiple zeta values of height one as examples.

scholarly journals Explicit formulas of alternating multiple zeta star values $ \zeta^\star({\bar 1}, \{1\}_{m-1}, {\bar 1}) $ and $ \zeta^\star(2, \{1\}_{m-1}, {\bar 1}) $

2021 ◽  
Vol 7 (1) ◽  
pp. 288-293
Author(s):  
Junjie Quan ◽  
Keyword(s):  
Multiple Zeta Values ◽  
Explicit Formulas ◽  
Recurrence Formulas ◽  
Multiple Zeta ◽  
Zeta Values

<abstract><p>In a recent paper <sup>[<xref ref-type="bibr" rid="b4">4</xref>]</sup>, Xu studied some alternating multiple zeta values. In particular, he gave two recurrence formulas of alternating multiple zeta values $ \zeta^\star({\bar 1}, \{1\}_{m-1}, {\bar 1}) $ and $ \zeta^\star(2, \{1\}_{m-1}, {\bar 1}) $. In this paper, we will give the closed forms representations of $ \zeta^\star({\bar 1}, \{1\}_{m-1}, {\bar 1}) $ and $ \zeta^\star(2, \{1\}_{m-1}, {\bar 1}) $ in terms of single zeta values and polylogarithms.</p></abstract>

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
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