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This commit is contained in:
Stefan Kebekus 2024-11-14 06:49:15 +01:00
parent 24bd4f9ffa
commit f43674dedc
2 changed files with 13 additions and 1 deletions
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11
Nevanlinna/analyticAt.lean
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@ -280,3 +280,14 @@ theorem analyticAt_finprod
exact Finset.analyticAt_prod h₁f.toFinset (fun a _ ↦ hf a) exact Finset.analyticAt_prod h₁f.toFinset (fun a _ ↦ hf a)
· rw [finprod_of_infinite_mulSupport h₁f] · rw [finprod_of_infinite_mulSupport h₁f]
exact analyticAt_const exact analyticAt_const
theorem AnalyticAt.zpow
{f : ℂ → ℂ}
{z₀ : ℂ}
{n : ℤ}
(h₁f : AnalyticAt ℂ f z₀)
(h₂f : f z₀ ≠ 0) :
AnalyticAt ℂ (fun x ↦ (f x) ^ n) z₀ := by
sorry

3
Nevanlinna/meromorphicOn_decompose.lean
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@ -68,12 +68,13 @@ theorem MeromorphicOn.decompose
· exact StronglyMeromorphicOn_of_makeStronglyMeromorphic h₁f z hz · exact StronglyMeromorphicOn_of_makeStronglyMeromorphic h₁f z hz
· right · right
use h₁f.divisor z use h₁f.divisor z
use (∏ᶠ p ≠ z, (fun x ↦ (x - p) ^ h₁f.divisor p)) * g use (∏ᶠ p : ({z}ᶜ : Set ℂ), (fun x ↦ (x - p.1) ^ h₁f.divisor p.1)) * g
constructor constructor
· apply AnalyticAt.mul₁ · apply AnalyticAt.mul₁
· apply analyticAt_finprod · apply analyticAt_finprod
intro w intro w
sorry sorry
· apply (h₃g z hz).analytic · apply (h₃g z hz).analytic
rw [h₂g ⟨z, hz⟩] rw [h₂g ⟨z, hz⟩]