Numerical method for computing Maass cusp forms on triply punctured two-sphere

Citation

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).

Abstract

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.

Download File

Preview

PDF (Abstract)
Numerical method for computing Maass cusp forms on triply punctured two-sphere.pdf
Download (35kB) | Preview

Additional Metadata

Item Type:	Conference or Workshop Item (Paper)
Divisions:	Faculty of Science Institute for Mathematical Research
DOI Number:	https://doi.org/10.1063/1.4866951
Publisher:	AIP Publishing LLC
Keywords:	Discrete eigenvalues; Maass cusp forms; Numerical method
Depositing User:	Nabilah Mustapa
Date Deposited:	26 Sep 2017 03:59
Last Modified:	26 Sep 2017 03:59
Altmetrics:	http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1063/1.4866951
URI:	http://psasir.upm.edu.my/id/eprint/57276
Statistic Details:	View Download Statistic

Actions (login required)

View Item