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
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
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