Theorems · Theorem · complex analysis

MeromorphicOn.divisor_pow

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {U : Set 𝕜} {f : 𝕜 → 𝕜},
  MeromorphicOn f U → ∀ (n : ℕ), MeromorphicOn.divisor (f ^ n) U = n • MeromorphicOn.divisor f U

If f is meromorphic, then the divisor of f ^ n is n times the divisor of f.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

2 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedField