erdos_516.limsup_ratio_eq_one

Let `f = ∑ aₖzⁿₖ` be an entire function such that `nₖ > k (log k) ^ (2 + c)`. Then `limsup (fun r => ratio r f) atTop = 1`. This is proved in [Ko65].

theorem erdos_516.limsup_ratio_eq_one {f : ℂ → ℂ} {n : ℕ → ℕ}
    (hn : ∃ c > (0 : ℝ), ∀ k, n k > k * log k ^ (2 + c)) {a : ℕ → ℂ} (ha : ∀ n, a n ≠ 0)
    (hfn : ∀ z, HasSum (fun k => a k * z ^ n k) (f z)) :
    limsup (fun r => ratio r f) atTop = 1

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