Note: Due to migration to google's new sites some of the animations are currently not working.

Zeros of the Selberg zeta function Z(β,α) for Γ₀(4) with character χ_α

This page is intended as a supplement to [1]. The animations below are based of certain numerical experiments that I performed during the preparation of my thesis [1]. The zeros of the Selberg zeta function Z(β,α) for the congruence subgroup Γ₀(4) are shown in the β-plane when the deformation parameter α changes. The zeros of this function are related to the discrete eigenvalues and the resonances of the hyperbolic Laplace-Beltrami operator on the corresponding surfaces of constant negative curvature. The main motivation for the investigation of such character deformations of the Selberg zeta function is that by studying the deformation of its zeros we gain access to the deformation of the discrete spectrum and the resonances of the hyperbolic Laplace-Beltrami operator, both under singular and non-singular perturbations. For more details and definition of the character χ_α see [1].

• Animation 1
• Animation 2
• Animation 3
• Animation 4

[1] Character deformation of the Selberg zeta function for congruence subgroups via the transfer operator; M. Fraczek, Ph.D. Thesis, (2012), PDF