$L$-derivatives of the fixed elliptic curve over rank-one imaginary quadratic fields

Shenghao Hua

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arXiv · 2507.20297

$L$-derivatives of the fixed elliptic curve over rank-one imaginary quadratic fields

Shenghao Hua

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Abstract

There is a one-sided central limit theorem for the logarithms of $L$-derivatives of a fixed rational non-CM elliptic curve $E$ over imaginary quadratic fields of rank one, analogous to a result of Radziwi\l\l\ and Soundararajan. There are also many $L$-derivatives that are not small.

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Shenghao Hua. 2025-07-27. $L$-derivatives of the fixed elliptic curve over rank-one imaginary quadratic fields. https://arxiv.org/abs/2507.20297

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