Numerical method for computing Maass cusp forms on triply punctured two-sphere
A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maa...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57276/ http://psasir.upm.edu.my/id/eprint/57276/1/Numerical%20method%20for%20computing%20Maass%20cusp%20forms%20on%20triply%20punctured%20two-sphere.pdf |
| _version_ | 1848853320475607040 |
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| author | Chan, Kar Tim Zainuddin, Hishamuddin Mohamed Kamari, Halimah |
| author_facet | Chan, Kar Tim Zainuddin, Hishamuddin Mohamed Kamari, Halimah |
| author_sort | Chan, Kar Tim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triply punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm. |
| first_indexed | 2025-11-15T10:52:06Z |
| format | Conference or Workshop Item |
| id | upm-57276 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:06Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-572762017-09-26T03:59:09Z http://psasir.upm.edu.my/id/eprint/57276/ Numerical method for computing Maass cusp forms on triply punctured two-sphere Chan, Kar Tim Zainuddin, Hishamuddin Mohamed Kamari, Halimah A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triply punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57276/1/Numerical%20method%20for%20computing%20Maass%20cusp%20forms%20on%20triply%20punctured%20two-sphere.pdf Chan, Kar Tim and Zainuddin, Hishamuddin and Mohamed Kamari, Halimah (2013) Numerical method for computing Maass cusp forms on triply punctured two-sphere. In: 4th International Meeting on Frontiers in Physics (IMFP 2013), 27-30 Aug. 2013, Kuala Lumpur, Malaysia. (pp. 230-235). 10.1063/1.4866951 |
| spellingShingle | Chan, Kar Tim Zainuddin, Hishamuddin Mohamed Kamari, Halimah Numerical method for computing Maass cusp forms on triply punctured two-sphere |
| title | Numerical method for computing Maass cusp forms on triply punctured two-sphere |
| title_full | Numerical method for computing Maass cusp forms on triply punctured two-sphere |
| title_fullStr | Numerical method for computing Maass cusp forms on triply punctured two-sphere |
| title_full_unstemmed | Numerical method for computing Maass cusp forms on triply punctured two-sphere |
| title_short | Numerical method for computing Maass cusp forms on triply punctured two-sphere |
| title_sort | numerical method for computing maass cusp forms on triply punctured two-sphere |
| url | http://psasir.upm.edu.my/id/eprint/57276/ http://psasir.upm.edu.my/id/eprint/57276/ http://psasir.upm.edu.my/id/eprint/57276/1/Numerical%20method%20for%20computing%20Maass%20cusp%20forms%20on%20triply%20punctured%20two-sphere.pdf |