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Mathematics of Computation

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Deformation of $ \Gamma_0(5)$-cusp forms

Author: Helen Avelin
Journal: Math. Comp. 76 (2007), 361-384
MSC (2000): Primary 11F72; Secondary 11F03, 11F06, 11Y35
Published electronically: October 4, 2006
MathSciNet review: 2261026
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Abstract: We develop an algorithm for numerical computation of the Eisenstein series on a Riemann surface of constant negative curvature. We focus in particular on the computation of the poles of the Eisenstein series. Using our numerical methods, we study the spectrum of the Laplace-Beltrami operator as the surface is being deformed. Numerical evidence of the destruction of $ \Gamma_0(5)$-cusp forms is presented.

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Additional Information

Helen Avelin
Affiliation: Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden

Received by editor(s): April 26, 2005
Received by editor(s) in revised form: January 30, 2006
Published electronically: October 4, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.