diff --git a/Nevanlinna/firstMain.lean b/Nevanlinna/firstMain.lean index f4b4e9a..abdfa50 100644 --- a/Nevanlinna/firstMain.lean +++ b/Nevanlinna/firstMain.lean @@ -1,21 +1,14 @@ -import Mathlib.Analysis.Analytic.Meromorphic -import Nevanlinna.holomorphic_JensenFormula +import Nevanlinna.divisor open Real -variable (f : ℂ → ℂ) -variable {h₁f : MeromorphicOn f ⊤} -variable {h₂f : f 0 ≠ 0} +noncomputable def Divisor.Nevanlinna.n + (D : Divisor ⊤) : + ℝ → ℤ := + fun r ↦ ∑ᶠ z ∈ Metric.ball (0 : ℂ) r, D z - -noncomputable def Nevanlinna.n : ℝ → ℤ := by - intro r - have : MeromorphicAt f z := by - exact h₁f (sorryAx ℂ true) trivial - exact ∑ᶠ z ∈ Metric.ball (0 : ℂ) r, (h₁f z trivial).order - -noncomputable def integratedCounting : ℝ → ℝ := by - intro r - -- Issue here: for s on the boundary of the ball, zero comes out. - exact ∑ᶠ s, (h₁f.order s).toNat * log (r * ‖s.1‖⁻¹) +noncomputable def Divisor.Nevanlinna.integratedCounting + (D : Divisor ⊤) : + ℝ → ℝ := + fun r ↦ ∑ᶠ z ∈ Metric.ball (0 : ℂ) r, (D z) * log (r * ‖z‖⁻¹)