Computation of Maass waveforms with nontrivial multiplier systems
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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 $0$.References
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Additional Information
- Fredrik Strömberg
- Affiliation: Institut für Theoretische Physik, TU Clausthal, Abteilung Statistische Physik und Nichtlineare Dynamik, Arnold-Sommerfeld-Strasse-6, 38678 Clausthal-Zellerfeld, Germany
- Address at time of publication: Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, 642 89 Darmstadt, Germany
- Email: stroemberg@mathematik.tu-darmstadt.de
- Received by editor(s): November 3, 2006
- Received by editor(s) in revised form: February 20, 2007
- Published electronically: May 15, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 2375-2416
- MSC (2000): Primary 11-04; Secondary 11F72, 11F37
- DOI: https://doi.org/10.1090/S0025-5718-08-02129-7
- MathSciNet review: 2429890