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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| Médium: | Článek |
| Jazyk: | English |
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Academic Publications
2009
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| On-line přístup: | http://psasir.upm.edu.my/id/eprint/13737/1/Computation%20of%20Maass%20cusp%20forms%20on%20modular%20group%20in%20Mathematica.pdf |
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| author | M. Siddig, Abubaker Ahmed Zainuddin, Hishamuddin |
| author_facet | M. Siddig, Abubaker Ahmed Zainuddin, Hishamuddin |
| author_sort | M. Siddig, Abubaker Ahmed |
| collection | UPM |
| 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.
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| first_indexed | 2024-03-06T07:29:14Z |
| format | Article |
| id | upm.eprints-13737 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:29:14Z |
| publishDate | 2009 |
| publisher | Academic Publications |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | M. Siddig, Abubaker Ahmed Zainuddin, Hishamuddin Computation of Maass cusp forms on modular group in Mathematica |
| title | 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_short | Computation of Maass cusp forms on modular group in Mathematica |
| title_sort | computation of maass cusp forms on modular group in mathematica |
| url | http://psasir.upm.edu.my/id/eprint/13737/1/Computation%20of%20Maass%20cusp%20forms%20on%20modular%20group%20in%20Mathematica.pdf |
| work_keys_str_mv | AT msiddigabubakerahmed computationofmaasscuspformsonmodulargroupinmathematica AT zainuddinhishamuddin computationofmaasscuspformsonmodulargroupinmathematica |