Year: 2026
Type: preprint
Abstract: Let $G$ be a connected semisimple real Lie group with finite center and let $(Γ_N)$ be a tower of cocompact lattices. We prove that the weak injective radius property implies the spherical density hypothesis with the same parameter. Together with the converse theorem of Golubev and Kamber, this gives an equivalence in the cocompact Archimedean setting. The proof uses a uniform spherical-mass estimate near spectral walls and a positive pre-trace kernel, but no tempered-spectrum estimate or a priori spectral gap.
Source: arXiv (Cornell University)
Author: Lutsko, Christopher
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216254103