Maass cusp form on asymmetric hyperbolic torus - Shamsuddin, Nor Syazana (2017)
The quantum system describing a free particle moving on a cusped hyperbolic surface is represented using the eigenfunction of the hyperbolic Laplace-Beltrami operator. The eigenspectra contained both continuous and discrete spectra, but the focus here is only on the discrete part. The eigenfunctions have to be computed numerically and they are known as Maass cusp form (MCF). The hyperbolic surface of interest here is the singly punctured two-torus. Past research has shown that the case of the symmetric torus has degenerate eigenvalues. The purpose of this research is to find the eigenvalues for asymmetric torus, deformed from symmetric torus by moving the vertices of its fundamental domain at the real axis, as well as to investigate the degeneracy behavior of its eigenvalues.