Some explicit values of a $q$-multiple zeta function at roots of unity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910943681708032 |
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| author | Komatsu, Takao |
| author_facet | Komatsu, Takao |
| contents | In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from generalizations of Stirling numbers. It is interesting, but by no means easy, to show the values explicitly in certain cases. We give explicit formulas by using Bell polynomials, determinants, $r$-Stirling numbers, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some explicit values of a $q$-multiple zeta function at roots of unity Komatsu, Takao Number Theory Combinatorics In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from generalizations of Stirling numbers. It is interesting, but by no means easy, to show the values explicitly in certain cases. We give explicit formulas by using Bell polynomials, determinants, $r$-Stirling numbers, etc. |
| title | Some explicit values of a $q$-multiple zeta function at roots of unity |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2505.09357 |