Loxodromic Eisenstein Series for Cofinite Kleinian Groups (Automorphic Forms, Automorphic L-Functions and Related Topics)

Abstract

We introduce an Eisenstein series associated to a loxodromic element of cofinite Kleinian groups, named the loxodromic Eisenstein series, and study its fundamental properties. We also establish the precise spectral expansion associated to the Laplace-Beltrami operator and derive the analytic continuation with the location of the possible poles and their residues. In addition, we study the asymptotic behavior of the loxodromic Eisenstein series for a degenerating sequence of fimite volume three-dimensional hyperbolic manifolds.