Selberg Zeta Functions and Transfer Operators

Introduction.-Preliminaries.-The Gamma function and the incomplete Gamma functions.-The Hurwitz Zeta Function and the Lerch Zeta Function.-Computation of the spectra and eigenvectors of large complex matrices.-The hyperbolic Laplace-Beltrami operator.-Transfer operators for the geodesic flow on hyperbolic surfaces.-Numerical results for spectra and traces of the transfer operator for character deformations.-Investigations of Selberg zeta functions under character deformations.-Concluding remarks.-Appendices.-References.-Index of Notations.

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• Análise numérica
• Teoria dos números
• Cálculo diferencial e equações
• Análise complexa, variáveis ??complexas
• Análise funcional e transforma
• Cibernética e teoria dos sistemas

Character deformation;Eigenvalues and resonances of hyperbolic Laplacian;Selberg zeta function;Singular perturbations of hyperbolic Laplacian;Transfer operator method