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Computation of Maass cusp forms on modular group in Mathematica

Maass cusp forms of the Fuchsian group are eigenfunctions of the hyperbolic Laplacian representing bound states. It is known that the Maass cusp forms can only be solved numerically. The aim of this paper is to ex-tend Hejhal's algorithm to compute Maass cusp form on the modular group SL(2, R)\...

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Main Authors: M. Siddig, Abubaker Ahmed, Zainuddin, Hishamuddin
Format: Article
Language:English
Published: Academic Publications 2009
Online Access:http://psasir.upm.edu.my/id/eprint/13737/1/Computation%20of%20Maass%20cusp%20forms%20on%20modular%20group%20in%20Mathematica.pdf
http://psasir.upm.edu.my/id/eprint/13737/
http://www.ijpam.eu/contents/2009-54-2/index.html
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spelling my.upm.eprints.137372015-10-22T06:08:19Z http://psasir.upm.edu.my/id/eprint/13737/ Computation of Maass cusp forms on modular group in Mathematica M. Siddig, Abubaker Ahmed Zainuddin, Hishamuddin Maass cusp forms of the Fuchsian group are eigenfunctions of the hyperbolic Laplacian representing bound states. It is known that the Maass cusp forms can only be solved numerically. The aim of this paper is to ex-tend Hejhal's algorithm to compute Maass cusp form on the modular group SL(2, R)\H using Mathematica with the intent of exploiting its graphical and symbolic capabilities. We compute the eigenvalues of the Maass cusp forms em-ploying a graphical scheme to locate the approximate value of the eigenvalue. We also plotted Maass cusp forms corresponding to selected eigenvalues. Academic Publications 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13737/1/Computation%20of%20Maass%20cusp%20forms%20on%20modular%20group%20in%20Mathematica.pdf M. Siddig, Abubaker Ahmed and Zainuddin, Hishamuddin (2009) Computation of Maass cusp forms on modular group in Mathematica. International Journal of Pure and Applied Mathematics, 54 (2). pp. 279-295. ISSN 1311-8080; ESSN: 1314-3395 http://www.ijpam.eu/contents/2009-54-2/index.html
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Maass cusp forms of the Fuchsian group are eigenfunctions of the hyperbolic Laplacian representing bound states. It is known that the Maass cusp forms can only be solved numerically. The aim of this paper is to ex-tend Hejhal's algorithm to compute Maass cusp form on the modular group SL(2, R)\H using Mathematica with the intent of exploiting its graphical and symbolic capabilities. We compute the eigenvalues of the Maass cusp forms em-ploying a graphical scheme to locate the approximate value of the eigenvalue. We also plotted Maass cusp forms corresponding to selected eigenvalues.
format Article
author M. Siddig, Abubaker Ahmed
Zainuddin, Hishamuddin
spellingShingle M. Siddig, Abubaker Ahmed
Zainuddin, Hishamuddin
Computation of Maass cusp forms on modular group in Mathematica
author_facet M. Siddig, Abubaker Ahmed
Zainuddin, Hishamuddin
author_sort M. Siddig, Abubaker Ahmed
title Computation of Maass cusp forms on modular group in Mathematica
title_short Computation of Maass cusp forms on modular group in Mathematica
title_full Computation of Maass cusp forms on modular group in Mathematica
title_fullStr Computation of Maass cusp forms on modular group in Mathematica
title_full_unstemmed Computation of Maass cusp forms on modular group in Mathematica
title_sort computation of maass cusp forms on modular group in mathematica
publisher Academic Publications
publishDate 2009
url http://psasir.upm.edu.my/id/eprint/13737/1/Computation%20of%20Maass%20cusp%20forms%20on%20modular%20group%20in%20Mathematica.pdf
http://psasir.upm.edu.my/id/eprint/13737/
http://www.ijpam.eu/contents/2009-54-2/index.html
_version_ 1643825421034192896
score 13.211869

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