The density Hypothesis for irreducible lattices in $\mathrm{PSL}_2(\mathbb{R})^d$

Dubi Kelmer

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arXiv · 2509.22595

The density Hypothesis for irreducible lattices in $\mathrm{PSL}_2(\mathbb{R})^d$

Dubi Kelmer

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Abstract

We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in $\mathrm{PSL}_2(\mathbb{R})^d$, extending previous results on the spherical density hypothesis to bound multiplicities of non-tempered non-spherical representations. Our bounds are uniform in the level as well as the spectral parameters.

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Dubi Kelmer. 2025-09-26. The density Hypothesis for irreducible lattices in $\mathrm{PSL}_2(\mathbb{R})^d$. https://arxiv.org/abs/2509.22595

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