Computation of Maass Waveforms with Non-trivial Multiplier Systems

Details Computation of Maass Waveforms with Non-trivial Multiplier Systems Computation of Maass Waveforms with Non-trivial Multiplier Systems

2006-11-06

arxiv.org/abs/math/0611146v1

Mathematics

Number Theory

39 pages, 6 figures

Scientific paper

The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group PSL(2,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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