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.
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More From: Proceedings of the Japan Academy, Series A, Mathematical Sciences
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