A probabilistic model for the distribution of ranks of elliptic curves over \(\mathbb{Q}\)

DOI10.1016/j.jnt.2020.05.022zbMath1469.11172arXiv1611.01999OpenAlexW3037334722MaRDI QIDQ2220456

Álvaro Lozano-Robledo

Publication date: 25 January 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.01999

zbMATH Keywords

elliptic curvesSelmer groupsprobabilistic modelCramer modelranks of elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52)

Related Items (1)

Two infinite families of elliptic curves with rank greater than one

Uses Software

• Magma
• SageMath

Cites Work

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• Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q
• Harald Cramér and the distribution of prime numbers
• Average rank of elliptic curves
• MOMENTS OF THE ORDERS OF TATE–SHAFAREVICH GROUPS
• On the order of magnitude of the difference between consecutive prime numbers

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