Deformations of Maass forms

Farmer, D.; Lemurell, S.

doi:10.1090/S0025-5718-05-01746-1

Deformations of Maass forms
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by D. W. Farmer and S. Lemurell PDF

Math. Comp. 74 (2005), 1967-1982 Request permission

Abstract:

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 Teichmüller 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.

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