The linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909317677973504 |
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| author | Calegari, Frank Dimitrov, Vesselin Tang, Yunqing |
| author_facet | Calegari, Frank Dimitrov, Vesselin Tang, Yunqing |
| contents | We prove the irrationality of the classical Dirichlet L-value $L(2,χ_{-3})$. The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier. In fact our work also establishes the $\mathbf{Q}$-linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$. We also give a number of other applications of our method to other problems in irrationality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$ Calegari, Frank Dimitrov, Vesselin Tang, Yunqing Number Theory We prove the irrationality of the classical Dirichlet L-value $L(2,χ_{-3})$. The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier. In fact our work also establishes the $\mathbf{Q}$-linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$. We also give a number of other applications of our method to other problems in irrationality. |
| title | The linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.15403 |