Open Access
Sept. 2001 Prime geodesic theorem via the explicit formula of $\Psi $ for hyperbolic 3-manifolds
Maki Nakasuji
Proc. Japan Acad. Ser. A Math. Sci. 77(7): 130-133 (Sept. 2001). DOI: 10.3792/pjaa.77.130

Abstract

We obtain a lower bound for the error term of the prime geodesic theorem for hyperbolic 3-manifolds. Our result is $\Omega_{\pm}(x(\log\log x)^{1/3} / \log x)$. We also generalize Sarnak's upper bound $O(x^{(5/3) + \varepsilon})$ to compact manifolds.

Citation

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Maki Nakasuji. "Prime geodesic theorem via the explicit formula of $\Psi $ for hyperbolic 3-manifolds." Proc. Japan Acad. Ser. A Math. Sci. 77 (7) 130 - 133, Sept. 2001. https://doi.org/10.3792/pjaa.77.130

Information

Published: Sept. 2001
First available in Project Euclid: 23 May 2006

zbMATH: 1028.11032
MathSciNet: MR1857290
Digital Object Identifier: 10.3792/pjaa.77.130

Subjects:
Primary: 11F72
Secondary: 11M36

Keywords: Explicit formula , lower bound , prime geodesic theorem

Rights: Copyright © 2001 The Japan Academy

Vol.77 • No. 7 • Sept. 2001
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