On the Prime Geodesic Theorem for Non-Compact Riemann Surfaces - Advances in Pure Mathematics

APM > Vol.6 No.12, November 2016

Advances in Pure Mathematics

Volume 6, Issue 12 (November 2016)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

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On the Prime Geodesic Theorem for Non-Compact Riemann Surfaces ()

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DOI: 10.4236/apm.2016.612068 1,253 Downloads 2,150 Views Citations

Author(s)

Muharem Avdispahić, Dženan Gušić

Affiliation(s)

Department of Mathematics, Faculty of Sciences and Mathematics, University of Sarajevo, Sarajevo, Bosnia and Herzegovina.

ABSTRACT

We use B. Randol’s method to improve the error term in the prime geodesic theorem for a noncompact Riemann surface having at least one cusp. The case considered is a general one, corresponding to a Fuchsian group of the first kind and a multiplier system with a weight on it.

KEYWORDS

Selberg Trace Formula, Selberg Zeta Function, Prime Geodesic Theorem

Share and Cite:

Avdispahić, M. and Gušić, D. (2016) On the Prime Geodesic Theorem for Non-Compact Riemann Surfaces. Advances in Pure Mathematics, 6, 903-914. doi: 10.4236/apm.2016.612068.

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