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Correlations for pairs of closed geodesics

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In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.

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Authors and Affiliations

  1. Department of Mathematics, Warwick University, Coventry, CV4 7AL, UK

    Mark Pollicott

  2. Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    Richard Sharp

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  1. Mark Pollicott
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  2. Richard Sharp
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Pollicott, M., Sharp, R. Correlations for pairs of closed geodesics. Invent. math. 163, 1–24 (2006). https://doi.org/10.1007/s00222-004-0427-7

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  • DOI: https://doi.org/10.1007/s00222-004-0427-7

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