# Determinants of Laplacians on Hilbert modular surfaces

## TL;DR

This paper investigates the regularized determinants of Laplacians on Hilbert modular surfaces, linking them to Selberg type zeta functions, thereby advancing understanding of spectral properties in this mathematical setting.

## Contribution

It establishes a connection between Laplacian determinants on Hilbert modular surfaces and Selberg type zeta functions, providing new insights into their spectral analysis.

## Key findings

- Determinants are expressed via Selberg type zeta functions
- Provides a spectral interpretation of Laplacian determinants
- Advances understanding of Hilbert modular surface spectra

## Abstract

We study regularized determinants of Laplacians acting on the space of Hilbert-Maass forms for the Hilbert modular group of a real quadratic field. We show that these determinants are described by Selberg type zeta functions introduced in [4,5].