The hyperbolic lattice point problem in conjugacy classes

2015/04/06 by Chatzakos, Dimitrios, Petridis, Yiannis
#11F72 (primary) #37C35 #37D40 (secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1504.01307

Abstract

For Γ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the Riemann surfaces Γ\backslash \mathbb H to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound O(X^2/3), due to A. Good. For \hboxSL(2,\mathbb Z) we interpret our results in terms of indefinite quadratic forms.

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