Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2012; 49(2): 367-372

Printed March 1, 2012

https://doi.org/10.4134/BKMS.2012.49.2.367

Copyright © The Korean Mathematical Society.

On the error term in the prime geodesic theorem

Muharem Avdispahi\'c and D\v zenan Gu\v si\'c

University of Sarajevo, University of Sarajevo

Abstract

Taking the integrated Chebyshev-type counting function of the appropriate order, we improve the error term in Park's prime geodesic theorem for hyperbolic manifolds with cusps. The obtained estimate coincides with the best known result in the Riemann surfaces case.

Keywords: Ruelle zeta function, prime geodesic theorem

MSC numbers: 11M36, 11F72

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