Publicacions Matemàtiques

Determinants of Laplacians on Hilbert modular surfaces

Yasuro Gon

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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 [5, 6].

Article information

Source
Publ. Mat., Volume 62, Number 2 (2018), 615-639.

Dates
Received: 27 January 2017
Revised: 18 April 2017
First available in Project Euclid: 16 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.pm/1529114426

Digital Object Identifier
doi:10.5565/PUBLMAT6221808

Mathematical Reviews number (MathSciNet)
MR3815289

Zentralblatt MATH identifier
06918957

Subjects
Primary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas 11F72: Spectral theory; Selberg trace formula 58J52: Determinants and determinant bundles, analytic torsion

Keywords
Hilbert modular surface Selberg zeta function regularized determinant

Citation

Gon, Yasuro. Determinants of Laplacians on Hilbert modular surfaces. Publ. Mat. 62 (2018), no. 2, 615--639. doi:10.5565/PUBLMAT6221808. https://projecteuclid.org/euclid.pm/1529114426


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