Spectral Data for Finite Volume Hyperbolic Surfaces at the Bottom of the Continuous Spectrum

Abstract

The spectrum of the Laplace operator on finite area non-compact surfaces becomes stable if one adjoins to the L 2 eigenvalues the scattering frequencies. For the bottom of the continuous spectrum ( 1 4 ) we need to take into account any non-vanishing Eisenstein series at s = 1 2 . In this work the particular behaviour of the spectrum at 1 4 is studied with respect to genericity of L 2 eigenvalues and of non-vanishing Eisenstein series at s = 1 2 .