Prime geodesic theorem for the Picard 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.

Two-geodesic transitive graphs of prime power order

In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be   $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...