Expected Mordell-Weil rank heuristics through Sato-Tate, Birch and Swinnerton-Dyer conjectures

2022/10/21 by Thakur, Dinesh S
#11G05 (Primary) 11G40 #14H52 #14K15 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.12028

Abstract

We present an heuristic argument for the prediction of expected Mordell-Weil rank of elliptic curves over number fields, using Birch and Swinnerton-Dyer's original conjecture and Sato-Tate conjectures. We do calculations in some cases and raise questions about their relations, if any, with the predictions of various average rank models that have been considered.

Related

• Elliptic curves with large rank over function fields
• Heuristics for the arithmetic of elliptic curves
• Elliptic curves with long arithmetic progressions have large rank
• A heuristic for boundedness of ranks of elliptic curves
• From the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture