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Deformations of Maass forms

Stefan Lemurell (Institutionen för matematiska vetenskaper, matematik)
Math. Comp. Vol. 74 (2005), 252, p. 1967-1982.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Maass forms, deformations, Phillips-Sarnak conjecture, Teichmuller space


Co-author: David Farmer



Denna post skapades 2007-10-03. Senast ändrad 2015-12-17.
CPL Pubid: 51021

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Algebra och geometri

Chalmers infrastruktur