Prime geodesic theorem for higher-dimensional hyperbolic manifold
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Abstract:
For a $(d+1)$-dimensional hyperbolic manifold $\mathcal {M}$, we consider an estimate of the error term of the prime geodesic theorem. Put the fundamental group $\Gamma$ of $\mathcal {M}$ to be a discrete subgroup of $SO_e(d+1, 1)$ with cofinite volume. When the contribution of the discrete spectrum of the Laplace-Beltrami operator is larger than that of the continuous spectrum in Weyl’s law, we obtained a lower estimate $\Omega _{\pm }(\tfrac {x^{d/2}(\log \log x)^{1/(d+1)}}{\log x})$ as $x$ goes to $\infty$.References
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Additional Information
- Maki Nakasuji
- Affiliation: Department of Mathematics, Keio University, 3-14-1 Hiyoshi, 223-8522, Japan
- Email: nakasuji@math.keio.ac.jp
- Received by editor(s): April 22, 2003
- Published electronically: March 24, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 3285-3303
- MSC (2000): Primary 11M36, 11F72
- DOI: https://doi.org/10.1090/S0002-9947-06-04122-5
- MathSciNet review: 2218976