Selberg type zeta function for the Hilbert modular group of a real quadratic field. (English) Zbl 1305.11077

Summary: In this article we announce fundamental results of Selberg type zeta functions for the Hilbert modular group of a real quadratic field; the meromorphic extension over \(\mathbb{C}\), its functional equation and some arithmetic applications.
Proofs are given in J. Number Theory 147, 396–453 (2015; Zbl 1380.11073).


11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
11F72 Spectral theory; trace formulas (e.g., that of Selberg)


Zbl 1380.11073
Full Text: DOI Euclid


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