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

Shenghao Hua

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

Number Theory 2026-01-05 v3

Authors: Shenghao Hua

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.

Keywords

L-derivatives elliptic curves imaginary quadratic fields central limit theorem rank-one fields

Cite

@article{arxiv.2507.20297,
  title  = {$L$-derivatives of the fixed elliptic curve over rank-one imaginary quadratic fields},
  author = {Shenghao Hua},
  journal= {arXiv preprint arXiv:2507.20297},
  year   = {2026}
}

Comments

A correct version for $L$-derivatives

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