Symmetry results for multiple $t$-values
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908281281183744 |
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| author | Charlton, Steven Hoffman, Michael E. |
| author_facet | Charlton, Steven Hoffman, Michael E. |
| contents | For a composition $I$ whose first part exceeds 1, we can define the multiple $t$-value $t(I)$ as the sum of all the terms in the series for the multiple zeta value $ζ(I)$ whose denominators are odd. In this paper we show that if $I$ is composition of $n\ge 3$, then $t(I)=(-1)^{n-1}t(\bar I)$ mod products, where $\bar I$ is the reverse of $I$, and both sides are suitably regularized when $I$ ends in 1. This result is not true for multiple zeta values, though there is an argument-reversal result that does hold for them (and for multiple $t$-values as well). We actually prove a more general version of this result, and then use it to establish explicit formulas for several classes of multiple $t$-values and interpolated multiple $t$-values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_14183 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symmetry results for multiple $t$-values Charlton, Steven Hoffman, Michael E. Number Theory Primary 11M32, 11G55, Secondary 33B30, 33B15 For a composition $I$ whose first part exceeds 1, we can define the multiple $t$-value $t(I)$ as the sum of all the terms in the series for the multiple zeta value $ζ(I)$ whose denominators are odd. In this paper we show that if $I$ is composition of $n\ge 3$, then $t(I)=(-1)^{n-1}t(\bar I)$ mod products, where $\bar I$ is the reverse of $I$, and both sides are suitably regularized when $I$ ends in 1. This result is not true for multiple zeta values, though there is an argument-reversal result that does hold for them (and for multiple $t$-values as well). We actually prove a more general version of this result, and then use it to establish explicit formulas for several classes of multiple $t$-values and interpolated multiple $t$-values. |
| title | Symmetry results for multiple $t$-values |
| topic | Number Theory Primary 11M32, 11G55, Secondary 33B30, 33B15 |
| url | https://arxiv.org/abs/2204.14183 |