Theorems · Theorem · complex analysis

MeromorphicOn.divisor_comp_sub_const_eq_divisor

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {U : Set 𝕜} {z : 𝕜} {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {c : 𝕜} {f : 𝕜 → E},
  (MeromorphicOn.divisor (f ∘ fun x => x - c) U) (z + c) = (MeromorphicOn.divisor f (U - {c})) z

Divisors are invariant under translation.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace