The Prime Geodesic Theorem

K. Soundararajan; Matthew P. Young

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The Prime Geodesic Theorem

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arxiv 1011.5486 v1 pith:3ILDRM2O submitted 2010-11-24 math.NT

The Prime Geodesic Theorem

K. Soundararajan , Matthew P. Young This is my paper

classification math.NT

keywords geodesicsprimecloseddirichletgeodesicl-functionstheoremcertain

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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.

The Prime Geodesic Theorem

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