The Schottky-Klein prime function and counting functions for Fenchel double crosses (Q2031032)

The author establishes a relation between problems of convergence of the classical Schottky-Klein prime function in complex analysis and a counting problem for pairs of geodesics in hyperbolic geometry studied by Fenchel. He associates to the counting problem an analytic function analogous to the Poincaré series and he solves the counting problem using ideas from ergodic theory and thermodynamic formalism.