This research demonstrates the density hypothesis for congruence subgroups in irreducible lattices, indicating significant extensions to prior theories.
We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in PSL₂(R)ᵈ, extending previous results on the spherical density hypothesis to include nonspherical representations. Our bounds are uniform in the level as well as the spectral parameters.
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Dubi Kelmer (2026) studied this question.
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