On pairs of prime geodesics with fixed homology difference

2006/04/12 by Morten S. Risager, Risager, Morten S.
Mathematics · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0604275

Abstract

We exhibit the analogy between prime geodesics on hyperbolic Riemann surfaces and ordinary primes. We present new asymptotic counting results concerning pairs of prime geodesics whose homology difference is fixed.

Related

• A norm on homology of surfaces and counting simple geodesics
• Prime geodesic theorem and closed geodesics for large genus
• Counting geodesics on prime-order k-differentials
• Counting geodesics of given commutator length
• A prime geodesic theorem for SL(4)