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arXiv · 2204.07602

The Distribution of Values of $\frac{L'}{L}(1/2+\epsilon,\chi_D)$

Alia Hamieh·Rory McClenagan
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Abstract

We determine the limiting distribution of the family of values $\frac{L'}{L}(1/2+\epsilon,\chi_D)$ as $D$ varies over fundamental discriminants. Here, $0<\epsilon<\frac12$, and $\chi_D$ is the real character associated with $D$. Moreover, we also establish an upper bound for the rate of convergence of this family to its limiting distribution. As a consequence of this result, we derive an asymptotic bound for the small values of $\left|\frac{L'}{L}(1/2+\epsilon,\chi_D)\right|$.

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Alia Hamieh, Rory McClenagan. 2022-04-15. The Distribution of Values of $\frac{L'}{L}(1/2+\epsilon,\chi_D)$. https://arxiv.org/abs/2204.07602

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