The Prime Geodesic Theorem

Abstract

We study the distribution of closed geodesics for the modular surface. We improve the error term in the prime geodesic theorem, and obtain results on prime geodesics in very short intervals conditionally on the generalized Riemann Hypothesis for Dirichlet L-functions. We emphasize a connection between the closed geodesics and certain Dirichlet L-functions.

arXiv comment13 pages

Cited by in corpus (3)

• $PGT$ on $PSL(2,\mathbb{Z})$. A short proof
• On Kuznetsov-Bykovskii's formula of counting prime geodesics
• The Prime Geodesic Theorem in Arithmetic Progressions