Theorems · Theorem · complex analysis

MeromorphicOn.divisor_comp_add_const_eq_divisor

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

Divisors are invariant under translation.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

2 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace