The Prime Geodesic Theorem in Arithmetic Progressions

Abstract

We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\uı-Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the reduced residue classes of a given modulus.

arXiv comment11 pages, LaTeX2e

References in corpus (9)

• The Prime Geodesic Theorem
• Mean square in the prime geodesic theorem
• Euler products of Selberg zeta functions in the critical strip
• On Kuznetsov-Bykovskii's formula of counting prime geodesics
• The Prime Geodesic Theorem for ${\mathrm{PSL}}_2(\mathbb{Z}[i])$ and Spectral Exponential Sums
• Spectral Exponential Sums on Hyperbolic Surfaces
• The prime geodesic theorem for the modular orbifold
• The Prime Geodesic Theorem for the Picard Orbifold
• Local square mean in the hyperbolic circle problem