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
    • Mathematics InstituteUniversity of Warwick

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.

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© Sociedade Brasileira de Matemática 1991