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arXiv · 2106.03682

$t$-adic symmetrization map on harmonic algebra

Masataka Ono
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Abstract

Bachmann, Takeyama and Tasaka introduced a $\mathbb{Q}$-linear map $\phi$, which we call the symmetrization map in this paper, on the harmonic algebra $\mathfrak{H}^1$. They calculated $\phi(w)$ explicitly for an element $w$ in $\mathfrak{H}^1$ related to the multiple zeta values of Mordell--Tornheim type. In this paper, we introduce its $t$-adic generalization $\widehat{\phi}$ and calculate $\widehat{\phi}(w)$ for an element $w$ in $\mathfrak{H}^1[[t]]$ constructed from the theory of $2$-colored rooted tree.

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Masataka Ono. 2021-06-07. $t$-adic symmetrization map on harmonic algebra. https://arxiv.org/abs/2106.03682

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