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.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3050