Prime geodesic theorem for higher-dimensional hyperbolic manifold

Author:
Maki Nakasuji

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

Published electronically:
March 24, 2006

MathSciNet review:
2218976

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Abstract: For a -dimensional hyperbolic manifold , we consider an estimate of the error term of the prime geodesic theorem. Put the fundamental group of to be a discrete subgroup of 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 as goes to .

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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

DOI:
https://doi.org/10.1090/S0002-9947-06-04122-5

Keywords:
Prime geodesic theorem,
Selberg zeta function,
Weyl's law

Received by editor(s):
April 22, 2003

Published electronically:
March 24, 2006

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.