# On Some Holomorphic Cohomological Equations

Abstract : 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
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Journal articles
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https://hal-uphf.archives-ouvertes.fr/hal-03148580
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Submitted on : Monday, February 22, 2021 - 12:52:41 PM
Last modification on : Tuesday, October 19, 2021 - 11:38:44 AM

### Citation

Aziz El Kacimi Alaoui. On Some Holomorphic Cohomological Equations. Results in Mathematics, Springer Verlag, 2013, 63 (1-2), pp.329-334. ⟨10.1007/s00025-011-0201-2⟩. ⟨hal-03148580⟩

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