Computation of Maass waveforms with nontrivial multiplier systems

Strömberg, Fredrik

doi:10.1090/S0025-5718-08-02129-7

Computation of Maass waveforms with nontrivial multiplier systems
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by Fredrik Strömberg PDF

Math. Comp. 77 (2008), 2375-2416 Request permission

Abstract:

The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group $PSL(2,\mathbb {Z})$ with general multiplier systems and real weight. A selection of numerical results obtained with these algorithms is also presented. Certain operators acting on the spaces of interest are also discussed. The specific phenomena that were investigated include the Shimura correspondence for Maass waveforms and the behavior of the weight-$k$ Laplace spectra for the modular surface as the weight approaches $0$.

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