IJPAM: Volume 54, No. 2 (2009)

COMPUTATION OF MAASS CUSP FORMS ON
MODULAR GROUP IN MATHEMATICA

Abubaker Ahmed M. Siddig$^1$, Hishamuddin Zainuddin$^2$Department of Physics, Faculty of Science, University Putra Malaysia, 43400 UPM, Serdang, Selangor, MALAYSIA
$^{1,2}$Institute for Mathematical Research
University Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^2$Department of Physics
Faculty of Science
University Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA


Abstract.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 extend Hejhal's algorithm to compute Maass cusp form on the modular group $\text{SL}(2,\mathbb{R})\backslash H$ using Mathematica with the intent of exploiting its graphical and symbolic capabilities. We compute the eigenvalues of the Maass cusp forms employing a graphical scheme to locate the approximate value of the eigenvalue. We also plotted Maass cusp forms corresponding to selected eigenvalues.

Received: June 11, 2009

AMS Subject Classification: 11F12, 65Y15, 11F7

Key Words and Phrases: maass cusp forms, Mathematica, modular group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 2