A proof of a weighted sum conjecture for finite multiple zeta values of level two

Zhonghua Li; Zhenlu Wang; Lihui Zhang

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arXiv · 2608.10675

A proof of a weighted sum conjecture for finite multiple zeta values of level two

Zhonghua Li·Zhenlu Wang·Lihui Zhang

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Abstract

M. Kaneko, T. Murakami and A. Yoshihara introduced finite multiple zeta values of level two and conjectured a weighted sum formula for indices whose components belong to $\{1,2\}$. In this paper, we use generating functions and linear recurrence relations to prove the conjecture. More precisely, we reduce the problem to a polynomial identity and solve the resulting second-order difference equation by identifying its specialized solutions with $_4F_3$ hypergeometric polynomials of Racah-type.

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Zhonghua Li, Zhenlu Wang, Lihui Zhang. 2026-08-11. A proof of a weighted sum conjecture for finite multiple zeta values of level two. https://arxiv.org/abs/2608.10675

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