Wikipedia · textbook · AMS 11 14
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Some conjectures about ranks of elliptic curves over ℚ
Theorem · card_heightLE_div_pow_five_div_six_tensto
Formula (5.1.1) of [PPVW2016]: The number of elliptic curves over ℚ with naïve height at most
H is asymptotically 2^(4/3)*3^(-3/2)/ζ(10) * H^(5/6).
Formal statement · Lean 4.lean
theorem card_heightLE_div_pow_five_div_six_tensto :
atTop.Tendsto (fun H ↦ (heightLE H).ncard / (H : ℝ) ^ (5 / 6 : ℝ))
(𝓝 (2 ^ (4 / 3 : ℝ) * 3 ^ (-3 / 2 : ℝ) / (riemannZeta 10).re)) := by
sorryProof. sorry
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