Folklore conjecture on ranks with prescribed torsion
Folklore conjecture on ranks with prescribed torsion
Let be a torsion group, and let denote the family of elliptic curves over with torsion subgroup prescribed by . Folklore conjecture on ranks with prescribed torsion. The proportion of elliptic curves with rank in and the proportion of elliptic curves with rank in are both . The conjecture predicts the minimalist rank distribution within every prescribed-torsion family; the source says that evenly distributed root numbers and the authors' one-level density results provide small evidence toward it, but gives no resolution.
Sources & referencesView supporting material
Primary source
Peter J. Cho and Keunyoung Jeong, “Average analytic rank of elliptic curves with prescribed torsion”, arXiv:2005.06862 (2021).
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