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Stefan Kebekus 2024-12-16 12:43:00 +01:00
parent cf301d65d6
commit 12397c3055
2 changed files with 21 additions and 5 deletions
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1
Nevanlinna/meromorphicOn.lean
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@ -2,7 +2,6 @@ import Mathlib.Analysis.Analytic.Meromorphic
import Nevanlinna.analyticAt import Nevanlinna.analyticAt
import Nevanlinna.divisor import Nevanlinna.divisor
import Nevanlinna.meromorphicAt import Nevanlinna.meromorphicAt
import Nevanlinna.meromorphicOn_divisor
import Nevanlinna.stronglyMeromorphicOn import Nevanlinna.stronglyMeromorphicOn
import Nevanlinna.mathlibAddOn import Nevanlinna.mathlibAddOn

25
Nevanlinna/meromorphicOn_divisor.lean
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@ -2,6 +2,7 @@ import Mathlib.Analysis.Analytic.Meromorphic
import Nevanlinna.analyticAt import Nevanlinna.analyticAt
import Nevanlinna.divisor import Nevanlinna.divisor
import Nevanlinna.meromorphicAt import Nevanlinna.meromorphicAt
import Nevanlinna.meromorphicOn
import Nevanlinna.stronglyMeromorphicOn import Nevanlinna.stronglyMeromorphicOn
@ -183,17 +184,33 @@ theorem StronglyMeromorphicOn.analyticOnNhd
tauto tauto
assumption assumption
theorem StronglyMeromorphicOn.support_divisor theorem StronglyMeromorphicOn.support_divisor
{f : ℂ → ℂ} {f : ℂ → ℂ}
{U : Set ℂ} {U : Set ℂ}
(hU : IsPreconnected U) (hU : IsConnected U)
(h₁f : StronglyMeromorphicOn f U) (h₁f : StronglyMeromorphicOn f U)
(h₂f : ∃ u ∈ U, f u ≠ 0) : (h₂f : ∃ u : U, f u ≠ 0) :
U ∩ f⁻¹' {0} = (Function.support h₁f.meromorphicOn.divisor) := by U ∩ f⁻¹' {0} = (Function.support h₁f.meromorphicOn.divisor) := by
ext u ext u
constructor constructor
· sorry · intro hu
unfold MeromorphicOn.divisor
simp [MeromorphicOn.order_ne_top hU h₁f h₂f ⟨u, hu.1⟩]
use hu.1
rw [(h₁f u hu.1).order_eq_zero_iff]
simp
exact hu.2
· intro hu · intro hu
simp at hu simp at hu
sorry let A := h₁f.meromorphicOn.divisor.supportInU hu
constructor
· exact h₁f.meromorphicOn.divisor.supportInU hu
· simp
let B := (h₁f u A).order_eq_zero_iff.not
simp at B
rw [← B]
unfold MeromorphicOn.divisor at hu
simp [A] at hu
exact hu.1