Deformation of Γ₀(5)-cusp forms

Avelin, Helen

doi:10.1090/S0025-5718-06-01911-9

Deformation of $\Gamma _0(5)$-cusp forms
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Math. Comp. 76 (2007), 361-384 Request permission

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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