Hyperbolic Eisenstein series for geometrically finite hyperbolic surfaces of infinite volume.

Thérèse Falliero (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

For a geometrically finite hyperbolic surface of infinite volume we write down the spectral decomposition for the Laplacian on 1-forms, generalize the Kudla and Millson's construction of hyperbolic Eisenstein series and other related results.

Mots clés: Harmonic differential; Eisenstein series; Degenerating surfaces Introduction

Domaines: Théorie spectrale [math.SP]

Thérèse Falliero. Hyperbolic Eisenstein series for geometrically finite hyperbolic surfaces of infinite volume.. Publications of the Research Institute for Mathematical Sciences, In press. ⟨hal-00610249v4⟩