A $q$-analogue of the Koecher-Leshchiner generating function of odd zeta values
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908669691559936 |
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| author | Tauraso, Roberto |
| author_facet | Tauraso, Roberto |
| contents | In the 1980s, Koecher and, independently, Leshchiner found an elegant formula for the generating function of odd zeta values. In this short note, we derive a $q$-analogue of this formula, which provides a $q$-version of the accelerated series for $ζ(3)$ used by Apéry in his famous proof of irrationality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $q$-analogue of the Koecher-Leshchiner generating function of odd zeta values Tauraso, Roberto Number Theory 11B65, 05A19, 05A15, 05A19, 05A30, 11M06 In the 1980s, Koecher and, independently, Leshchiner found an elegant formula for the generating function of odd zeta values. In this short note, we derive a $q$-analogue of this formula, which provides a $q$-version of the accelerated series for $ζ(3)$ used by Apéry in his famous proof of irrationality. |
| title | A $q$-analogue of the Koecher-Leshchiner generating function of odd zeta values |
| topic | Number Theory 11B65, 05A19, 05A15, 05A19, 05A30, 11M06 |
| url | https://arxiv.org/abs/2511.18034 |