On Some Holomorphic Cohomological Equations
Résumé
Let Σ be a non compact Riemann surface and γ:Σ⟶Σ an automorphism acting freely and properly such that the quotient M = Σ/γ is a non compact Riemann surface. Using the fact that Σ and M are Stein manifolds, we prove that, for any holomorphic function g:Σ⟶C and any λ∈C , there exists a holomorphic function f:Σ⟶C which is a solution of the holomorphic cohomological equation f∘γ−λf=g