Hyperbolic Eisenstein series on [formula omitted]-dimensional hyperbolic spaces

Abstract

We define a generalized hyperbolic Eisenstein series for a pair of a hyperbolic manifold of finite volume and its submanifold. We prove the convergence, the differential equation and the precise spectral expansion associated to the Laplace–Beltrami operator. We also derive the analytic continuation with the location of the possible poles and their residues from the spectral expansion.