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arXiv · 2408.15403

The linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$

Frank Calegari·Vesselin Dimitrov·Yunqing Tang
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Abstract

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.

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Frank Calegari, Vesselin Dimitrov, Yunqing Tang. 2024-08-27. The linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$. https://arxiv.org/abs/2408.15403

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