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Computing Maass cusp form on general hyperbolic torus


Citation

Shamsuddin, Nor Syazana and Zainuddin, Hishamuddin and Chan, Kar Tim (2016) Computing Maass cusp form on general hyperbolic torus. In: 2nd International Conference and Workshop on Mathematical Analysis (ICWOMA 2016), 2-4 Aug. 2016, Langkawi, Malaysia. (pp. 1-8).

Abstract

The bound states of a quantum mechanical system on a punctured hyperbolic torus are described by Maass cusp forms, which are eigenfunctions of the hyperbolic Laplace-Beltrami operator vanishing at infinity. In a recent work by Chan et al. (2013), the computation of Maass cusp forms makes use of the symmetric fundamental domain for the hyperbolic torus. As a result, the Maass cusp forms then are divided into odd and even classes. It is of interest to consider the case when no symmetry is assumed. This requires the expansion of Maass cusp form in its complex Fourier form. In this paper, we show the available algorithm can be extended to employ directly the complex Fourier expansion using Mathematica. We were able to reproduce the results of Chan et al, on the symmetric hyperbolic torus but now with the capability of applying the algorithm even for the case of asymmetric hyperbolic torus.


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Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1063/1.4972158
Publisher: AIP Publishing
Keywords: Maass cusp; Hyperbolic torus; Symmetry
Depositing User: Nabilah Mustapa
Date Deposited: 26 Sep 2017 03:48
Last Modified: 26 Sep 2017 03:48
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4972158
URI: http://psasir.upm.edu.my/id/eprint/57260
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