On the convolutions of sums of multiple zeta(-star) values of height one

2021/10/01 by Kwang-Wu Chen, Chen, Kwang-Wu, Minking Eie +1
Mathematics · #33B15 #FOS: Mathematics #Number Theory (math.NT) #Primary 11M32 #Secondary: 05A15 #math.NT #msc:05A15 #msc:11M32 #msc:33B15

paper · pdf · doi:10.48550/arxiv.2110.00231

Any comments are welcome

arxiv created 2021/10/01 · arxiv updated 2021/10/04

Abstract

In this paper, we investigate the sums of mutliple zeta(-star) values of height one: Z_±(n)=∑_a+b=n (± 1)^bζ(\1\^a,b+2), Z_±^⋆(n)=∑_a+b=n (± 1)^bζ^⋆(\1\^a,b+2). In particular, we prove that the weighted sum ∑_\substack0≤ m≤ p m: \rm even ∑_{|\boldsymbolα|=p+3} 2^α_m+1 +1ζ(α₀,α₁,…,α_m,α_m+1+1) can be evaluated through the convolution of Z_-(m) and Z₊(n) with m+n=p.

Related

• On three general forms of multiple zeta(-star) values
• Sum formulas of mltiple zeta values with arguments are multiple of a positive integer
• Weighted Sum Formulas from Shuffle Products of Multiple Zeta-star Values
• A combinatorial proof of the weighted sum formula for finite and symmetric multiple zeta(-star) values
• Weighted sum formulas of multiple zeta values with even arguments