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 [5, 6].
Yasuro Gon. "Determinants of Laplacians on Hilbert modular surfaces." Publ. Mat. 62 (2) 615 - 639, 2018. https://doi.org/10.5565/PUBLMAT6221808