Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society

, Volume 21, Issue 2, pp 205–229

An analogue of Mertens' theorem for closed orbits of Axiom A flows

  • Richard Sharp

DOI: 10.1007/BF01237365

Cite this article as:
Sharp, R. Bol. Soc. Bras. Mat (1991) 21: 205. doi:10.1007/BF01237365


For an Axiom A flow restricted to a basic set we prove an analogue of Mertens' theorem of prime number theory. The result is also established for the geodesic flow on a non-compact, finite area surface of constant negative curvature. Applying this to the modular surface yields some asymptotic formulae concerning quadratic forms.

Copyright information

© Sociedade Brasileira de Matemática 1991

Authors and Affiliations

  • Richard Sharp
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryEngland