The Prime Geodesic Theorem

Details The Prime Geodesic Theorem The Prime Geodesic Theorem

2010-11-24

arxiv.org/abs/1011.5486v1

Mathematics

Number Theory

13 pages

Scientific paper

We study the distribution of closed geodesics for the modular surface. We
improve the error term in the prime geodesic theorem, and obtain results on
prime geodesics in very short intervals conditionally on the generalized
Riemann Hypothesis for Dirichlet L-functions. We emphasize a connection between
the closed geodesics and certain Dirichlet L-functions.

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