Prime number theorems for Basmaijan-type identities

Basmajian identity expresses the volume of the boundary of a compact
hyperbolic manifold as a sum over the orthogeodesics on the manifold. In
the spirit of Dirichlet’s unit theorem, we introduce Hecke-type L-functions
coming from Basmajian identities for Schottky groups and quadratic
polynomials. We discuss their applications to counting (complex)
orthospectrum, equidistribution of holonomy and orbit counting in complex
dynamics.