The linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$
| Autor: | Calegari, Frank, Dimitrov, Vesselin, Tang, Yunqing |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove the irrationality of the classical Dirichlet L-value $L(2,\chi_{-3})$. 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 $1$, $\zeta(2)$, and $L(2,\chi_{-3})$. We also give a number of other applications of our method to other problems in irrationality. Comment: 218 pages, comments welcome, minor expository changes, this is the submitted version of the paper |
| Databáze: | arXiv |
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