Title :

LES FORMES AUTOMORPHES FEUILLETÉES

Author(s) :

Otal, Jean-Pierre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

HAL domain(s) :

Mathématiques [math]/Théorie spectrale [math.SP]
Mathématiques [math]/Géométrie différentielle [math.DG]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Français

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL