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arXiv · 1504.01307

The hyperbolic lattice point problem in conjugacy classes

Dimitrios Chatzakos·Yiannis Petridis
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Abstract

For $\Gamma$ 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 $\Gamma\backslash \mathbb H$ 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 $\hbox{SL}(2,{\mathbb Z})$ we interpret our results in terms of indefinite quadratic forms.

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Dimitrios Chatzakos, Yiannis Petridis. 2015-04-06. The hyperbolic lattice point problem in conjugacy classes. https://arxiv.org/abs/1504.01307

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