Deformations of Maass forms
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We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface $S$ under deformation of the surface. Our calculations indicate that if the Teichmuller space of $S$ is not trivial then each cusp form has a set of deformations under which either the cusp form remains a cusp form, or else it dissolves into a resonance whose constant term is uniformly a factor of $10^{8}$ smaller than a typical Fourier coefficient of the form. We give explicit examples of those deformations in several cases.
AMSTeX, 16 pages, 13 figures. Final version, to appear in Math. Comp
AMSTeX, 16 pages, 13 figures. Final version, to appear in Math. Comp