rank_height_count_asymptotic

[PPVW2016] 8.2(b): for 1 ≤ r ≤ 20, the number of elliptic curves over ℚ with rank `r` and naïve height at most `H` is asymptotically `H ^ ((21 - r) / 24 + o(1))`. Note: ℰ_H in 8.2(b) should be ℰ_{≤H}, see the statement of Theorem 7.3.3. When `r = 1`, the exponent is `20 / 24 = 5 / 6`, which agrees with the exponent in `card_heightLE_div_pow_five_div_six_tensto` and is consistent with `half_rank_zero_and_half_rank_one`.

theorem rank_height_count_asymptotic (r : ℕ) (h₁ : 1 ≤ r) (h₂ : r ≤ 20) :
    ∃ f : ℕ → ℝ, atTop.Tendsto f (𝓝 0) ∧
      ∀ H : ℕ, 1 < H → {E ∈ heightLE H | r ≤ E.rank}.ncard = (H : ℝ) ^ ((21 - r) / 24 + f H)

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