Abstract: We explore the pair correlation density for angles in hyperbolic lattices through a detailed exposition of the work of Kelmer and Kontorovich. Given a lattice Γ < PSL2(R) and a basepoint ω in the upper half plane H, Kelmer and Kontorovich prove the existence of a limiting pair correlation density function for the angles formed by geodesics connecting ω to points in Γω, and provide an explicit formula for it. Their result resolves a conjecture posed by Boca, Popa, and Zaharescu, using tools from the theory of automorphic forms and spectral analysis. We outline their findings by following the structure of their paper On The Pair Correlation Density of Hyperbolic Angles and expand on key technical details throughout.
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