Pair correlation of angles between reciprocal geodesics on the modular surface
The authors prove a limit theorem for the pair correlation for angels between reciprocal geodesics on the modular surface. The main result gives a completely explicit formula for the pair correlation function containing natural geometric quantities. The method also gives further insight in the associated reciprocal classes of binary quadratic forms. The authors nicely explain the concept of reciprocal geodesics in the context of the underlying hyperbolic structure. The proof of the main result is rather elaborate, however the result itself is very interesting, since it is completely different from the Euclidean situation.
scientific article; zbMATH DE number 6331629