$t$-adic symmetric multiple zeta values for indices with alternating $1$ and $3$, starting with $1$ and ending with $3$

Kento Fujita

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arXiv · 2503.08380

$t$-adic symmetric multiple zeta values for indices with alternating $1$ and $3$, starting with $1$ and ending with $3$

Kento Fujita

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Abstract

Hirose, Murahara, and Saito proved that some $t$-adic symmetric multiple zeta values, for indices in which $1$ and $3$ appear alternately in succession, can be expressed as polynomials in Riemann zeta values, and conjectured similar formulas. In this paper, we prove the conjectured formula for indices that start with $1$ and end with $3$, showing that they also can be expressed as polynomials in Riemann zeta values.

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BibTeX RIS

Kento Fujita. 2025-03-11. $t$-adic symmetric multiple zeta values for indices with alternating $1$ and $3$, starting with $1$ and ending with $3$. https://arxiv.org/abs/2503.08380

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