Bowman-Bradley type theorem for finite multiple zeta values in $\mathcal{A}_2$

Hideki Murahara; Tomokazu Onozuka; Shin-ichiro Seki

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arXiv · 1810.10803

Bowman-Bradley type theorem for finite multiple zeta values in $\mathcal{A}_2$

Hideki Murahara·Tomokazu Onozuka·Shin-ichiro Seki

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Abstract

Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two kinds of the strings $\{1,3,\ldots,1,3\}$ and $\{2,\ldots,2\}$ is a rational multiple of a power of $\pi^2$. Recently, Saito and Wakabayashi proved that analogous but more general sums of finite multiple zeta values in an adelic ring $\mathcal{A}_1$ vanish. In this paper, we partially lift Saito-Wakabayashi's theorem from $\mathcal{A}_1$ to $\mathcal{A}_2$. Our result states that a Bowman-Bradley type sum of finite multiple zeta values in $\mathcal{A}_2$ is a rational multiple of a special element and this is closer to the original Bowman-Bradley theorem.

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Hideki Murahara, Tomokazu Onozuka, Shin-ichiro Seki. 2018-10-25. Bowman-Bradley type theorem for finite multiple zeta values in $\mathcal{A}_2$. https://arxiv.org/abs/1810.10803

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