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arXiv · 2509.05473

Extreme values of class group $L$-functions

João C. C. Vargas
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Abstract

We give a lower bound for the maximum value of class group $L$-functions attached to $\mathbb{Q}(\sqrt{-D})$ at the central point and show that this value is on average at least $$\exp\Bigg(\delta\sqrt{\frac{\log D \log \log \log D}{\log \log D}} \Bigg)$$ for any $\delta < \frac{1}{4}$.

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João C. C. Vargas. 2025-09-05. Extreme values of class group $L$-functions. https://arxiv.org/abs/2509.05473

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