Some conjectures about ranks of elliptic curves over ℚ
[PPVW2016] 8.2(c): the number of elliptic curves over ℚ with rank ≥ 21 and naïve height at most H is asymptotically at most H ^ o(1).
Mathematical statement
[PPVW2016] 8.2(c): the number of elliptic curves over ℚ with rank ≥ 21 and naïve height
at most H is asymptotically at most H ^ o(1).
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
Attributed source material. Reuse must follow the linked attribution and share-alike terms.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
twentyone_le_rank_height_count_asymptotic
theorem twentyone_le_rank_height_count_asymptotic : ∃ f : ℕ → ℝ, atTop.Tendsto f (𝓝 0) ∧ ∀ H : ℕ, 1 < H → {E ∈ heightLE H | 21 ≤ E.rank}.ncard ≤ (H : ℝ) ^ f H := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References