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arXiv · 2508.12205

Large values of quadratic Dirichlet $L$-functions near the central point

Zikang Dong·Zhonghua Li·Yutong Song·Shengbo Zhao
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Abstract

In this paper, we investigate the conditional large values of the quadratic Dirichlet $L$-functions near the central point $s=1/2$. When $\sigma $ closes to $1/2$ within a suitable range, we show that $L(\sigma, \chi_d)$ have the conditional large values of the similar order of magnitude as $L(1/2, \chi_d)$.

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Zikang Dong, Zhonghua Li, Yutong Song, Shengbo Zhao. 2025-08-17. Large values of quadratic Dirichlet $L$-functions near the central point. https://arxiv.org/abs/2508.12205

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