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.
Publié le : 2001-09-14
Classification:
Lower bound,
prime geodesic theorem,
explicit formula,
11F72,
11M36
@article{1148393038,
author = {Nakasuji, Maki},
title = {Prime geodesic theorem via the explicit formula of $\Psi $ for hyperbolic 3-manifolds},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {77},
number = {10},
year = {2001},
pages = { 130-133},
language = {en},
url = {http://dml.mathdoc.fr/item/1148393038}
}
Nakasuji, Maki. Prime geodesic theorem via the explicit formula of $\Psi $ for hyperbolic 3-manifolds. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp. 130-133. http://gdmltest.u-ga.fr/item/1148393038/