Average rank of quadratic twists with a rational point of almost minimal height

2020/11/26 by Joachim L. Petit, Petit, Joachim
Mathematics · #11D45 #11G05 #11G50 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2011.13195

openalex publication_date 2020/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a family of quadratic twists of a fixed elliptic curve defined over ℚ, we investigate the average rank in the subfamily of twists having a nontorsion rational point of almost minimal height. We show in particular that the average analytic rank is greater than one.

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