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Mathematics of Computation

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Computation of Maass waveforms with nontrivial multiplier systems


Author: Fredrik Strömberg
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
Published electronically: May 15, 2008
MathSciNet review: 2429890
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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.


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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

DOI: https://doi.org/10.1090/S0025-5718-08-02129-7
Keywords: Maass waveforms, multiplier systems, computational spectral theory, Shimura correspondence, Hecke operators
Received by editor(s): November 3, 2006
Received by editor(s) in revised form: February 20, 2007
Published electronically: May 15, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.