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arXiv · 1208.5955

Hybrid trace formula for a non-uniform irreducible lattice in $\PSL_2(\bbR)^n$

Dubi Kelmer
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Abstract

In a series of lectures Selberg introduced a trace formula on the space of hybrid Maass-modular forms of an irreducible uniform lattice in $\PSL_2(\bbR)^n$. In this paper we derive the analogous formula for a non-uniform lattice and use it to study the distribution of elliptic-hyperbolic conjugacy classes. In particular, for Hilbert modular groups there is a nice interpretation of these results in terms of class numbers and fundamental units of quadratic forms over totally real number fields.

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Dubi Kelmer. 2012-08-29. Hybrid trace formula for a non-uniform irreducible lattice in $\PSL_2(\bbR)^n$. https://arxiv.org/abs/1208.5955

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