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Deformations of Maass forms
Author(s):
D.
W.
Farmer;
S.
Lemurell.
Journal:
Math. Comp.
74
(2005),
1967-1982.
MSC (2000):
Primary 11F03;
Secondary 11F30
Posted:
April 15, 2005
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Abstract:
We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface  under deformation of the surface. Our calculations indicate that if the Teichmüller space of  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  smaller than a typical Fourier coefficient of the form. We give explicit examples of those deformations in several cases.
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Additional Information:
D.
W.
Farmer
Affiliation:
American Institute of Mathematics, 360 Portage Avenue, Palo Alto, California 94307
Email:
farmer@aimath.org
S.
Lemurell
Affiliation:
Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Email:
sj@math.chalmers.se
DOI:
10.1090/S0025-5718-05-01746-1
PII:
S 0025-5718(05)01746-1
Keywords:
Maass forms,
deformations,
Phillips-Sarnak conjecture,
Teichmuller space
Received by editor(s):
February 19, 2003
Received by editor(s) in revised form:
April 30, 2004
Posted:
April 15, 2005
Additional Notes:
Research of the first author was supported in part by the National Science Foundation and the American Institute of Mathematics.
Research of the second author was supported in part by ``Stiftelsen för internationalisering av högre utbildning och forskning'' (STINT)
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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