Deformations of Maass forms
Journal article, 2005

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 Teichm├╝ller 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.

Phillips-Sarnak conjecture

Teichmuller space


Maass forms


Stefan Lemurell

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Math. Comp.

Vol. 74 252 1967-1982

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