Prime geodesic theorem for higher-dimensional hyperbolic manifold

The prime geodesic theorem for higher rank spaces

The prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula that is based on work of Andreas Juhl.

A prime geodesic theorem for higher rank spaces

A prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula for higher rank torus actions.

A prime geodesic theorem for higher rank II: singular geodesics

Ruelle zeta function and Prime geodesic theorem for hyperbolic manifolds with cusps

For a d-dimensional real hyperbolic manifold with cusps, we obtain more refined error terms in the prime geodesic theorem (PGT) using the Ruelle zeta function instead of the Selberg zeta function. To do this, we prove that the Ruelle zeta function over this type manifold is a meromorphic function of order d over C.

Immersing almost geodesic surfaces in a closed hyperbolic three manifold

Let M be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into M so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.