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arXiv · 1609.09168

Finite multiple zeta values associated with 2-colored rooted trees

Masataka Ono
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Abstract

We define finite multiple zeta values (FMZVs) associated with some combinatorial objects, which we call 2-colored rooted trees, and prove that FMZVs associated with 2-colored rooted trees satisfying certain mild assumptions can be written explicitly as $\mathbb{Z}$-linear combinations of the usual FMZVs. Our result can be regarded as a generalization of Kamano's recent work on finite Mordell-Tornheim multiple zeta values. As an application, we will give a new proof of the shuffle relation of FMZVs, which was first proved by Kaneko and Zagier.

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Masataka Ono. 2016-09-29. Finite multiple zeta values associated with 2-colored rooted trees. https://arxiv.org/abs/1609.09168

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