Computation of Eigenvalues, Spectral Zeta Functions and Zeta-Determinants on Hyperbolic Surfaces

TL;DR

This paper explains the mathematical methods for computing eigenvalues and spectral determinants on hyperbolic surfaces, focusing on their theoretical foundations in geometrically complex settings.

Contribution

It provides a detailed exposition of the mathematical theory behind spectral computations on hyperbolic surfaces, bridging geometry and spectral analysis.

Findings

Clarifies the mathematical framework for spectral computations

Connects spectral theory with hyperbolic geometry

Provides insights into spectral determinants on complex surfaces

Abstract

These are lecture notes from a series of three lectures given at the summer school "Geometric and Computational Spectral Theory" in Montreal in June 2015. The aim of the lecture was to explain the mathematical theory behind computations of eigenvalues and spectral determinants in geometrically non-trivial contexts.