import Nevanlinna.holomorphic


def zeroDivisor
  {f : ℂ → ℂ}
  {R : ℝ}
  (h₁f : ∀ z ∈ Metric.closedBall z R, HolomorphicAt f z)
  (h₂f : ∃ z ∈ Metric.closedBall z R, f z ≠ 0) :
  ℂ → ℕ := by
  sorry