Distribution of prime geodesic traces
Anton Deitmar
TL;DR
This paper improves the error term estimate in the distribution of prime geodesic traces using a Dirichlet style Prime Geodesic Theorem and the Selberg trace formula, enhancing understanding of geodesic trace distribution.
Contribution
It provides an improved error estimate for prime geodesic trace distribution by applying a Dirichlet style Prime Geodesic Theorem and the Selberg trace formula.
Findings
Enhanced error term estimate in prime geodesic trace distribution
Application of Dirichlet style Prime Geodesic Theorem
Use of Selberg trace formula for proof
Abstract
This note complements a recent paper of Chatzakos, Harcos and Kaneko \cite{CHK}. We use a Dirichlet style Prime Geodesic Theorem to improve the error term estimate in loc. cit. at the cost of lowering the resolution. The proof relies on the Selberg trace formula.
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Taxonomy
TopicsGeometry and complex manifolds · Analytic Number Theory Research · Analytic and geometric function theory