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Pré-Publication, Document De Travail Année : 2019

LES FORMES AUTOMORPHES FEUILLETÉES

Résumé

We introduce a family {Bs(Γ)} s∈C of line bundles over the unit tangent bundle T 1 XΓ of a hyperbolic surface XΓ. These bundles vary in an holomorphic way when restricted to the leaves of the stable foliation and to the leaves of the unstable foliation. A stable (resp. unstable) foliated automorphic form of weight s on T 1 XΓ is defined as a continuous section of Bs(Γ) → T 1 XΓ which is holomorphic along the leaves of the stable (resp. unstable) foliation. We study mainly the case when XΓ is compact. In that situation we construct, from any s(1 − s)-eigenfunction of the Laplace operator on XΓ, two foliated automorphic forms, one of weight s and one of weight 1 − s. We give some general properties of the foliated automorphic forms ; in particular, we construct when 0 < s < 1, an isomorphism between the spaces As(Γ) et A1−s(Γ) of the stable automorphic forms of respective weights s and 1 − s.
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Dates et versions

hal-01978942 , version 1 (11-01-2019)

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  • HAL Id : hal-01978942 , version 1

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Jean-Pierre Otal. LES FORMES AUTOMORPHES FEUILLETÉES. 2019. ⟨hal-01978942⟩
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