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

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Abstract

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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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV47AL, Coventry, England

    Richard Sharp

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  1. Richard Sharp
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Supported by S.E.R.C. grant no. 88001623.

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Sharp, R. An analogue of Mertens' theorem for closed orbits of Axiom A flows. Bol. Soc. Bras. Mat 21, 205–229 (1991). https://doi.org/10.1007/BF01237365

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  • DOI: https://doi.org/10.1007/BF01237365

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