$t$-adic symmetric multiple zeta values for indices with alternating $1$ and $3$, starting with $1$ and ending with $3$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909544713551872 |
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| author | Fujita, Kento |
| author_facet | Fujita, Kento |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $t$-adic symmetric multiple zeta values for indices with alternating $1$ and $3$, starting with $1$ and ending with $3$ Fujita, Kento Number Theory 11M32 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. |
| title | $t$-adic symmetric multiple zeta values for indices with alternating $1$ and $3$, starting with $1$ and ending with $3$ |
| topic | Number Theory 11M32 |
| url | https://arxiv.org/abs/2503.08380 |