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arXiv · 2212.13360

Extreme central $L$-values of almost prime quadratic twists of elliptic curves

Shenghao Hua·Bingrong Huang
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Abstract

In this paper, we prove the extreme values of $L$-functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme values for the Tate--Shafarevich groups in the quadratic twist family of an elliptic curve under the Birth--Swinnerton-Dyer conjecture.

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Shenghao Hua, Bingrong Huang. 2022-12-27. Extreme central $L$-values of almost prime quadratic twists of elliptic curves. https://doi.org/10.1007/s11425-022-2216-y

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