Algebraic identities among $q$- analogue of Euler double zeta values
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909166780547072 |
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| author | Chatterjee, Tapas Garg, Sonam |
| author_facet | Chatterjee, Tapas Garg, Sonam |
| contents | In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant. Using a $q$-analogue of the Nielsen Reflexion Formula for $q>1$, we investigate identities involving different versions of $q$-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of $ζ_q(s_1, s_2)$ as $s_1$ and $s_2$ approach to $0$ and compare these limits to those of the classical double-zeta function. Finally, we discuss the $q$-analogue of the Mordell-Tornheim $r$-ple zeta function and its relation with the $q$-double zeta function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic identities among $q$- analogue of Euler double zeta values Chatterjee, Tapas Garg, Sonam Number Theory In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the variants of $q$-double zeta function. This article focuses on exploring identities related to another variant of $q$-double zeta function and its star variant. Using a $q$-analogue of the Nielsen Reflexion Formula for $q>1$, we investigate identities involving different versions of $q$-analogues of the Riemann zeta function and the double-zeta function. Additionally, we analyze the behavior of $ζ_q(s_1, s_2)$ as $s_1$ and $s_2$ approach to $0$ and compare these limits to those of the classical double-zeta function. Finally, we discuss the $q$-analogue of the Mordell-Tornheim $r$-ple zeta function and its relation with the $q$-double zeta function. |
| title | Algebraic identities among $q$- analogue of Euler double zeta values |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.07688 |