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

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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.

Supported by S.E.R.C. grant no. 88001623.