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The hyperbolic lattice point problem in conjugacy classes

Chatzakos, D; Petridis, Y; (2016) The hyperbolic lattice point problem in conjugacy classes. Forum Mathematicum , 28 (5) pp. 981-1003. 10.1515/forum-2015-0102. Green open access

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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∖ℍ to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound O(X2/3), due to Good. For SL2(ℤ) we interpret our results in terms of indefinite quadratic forms.

Type: Article
Title: The hyperbolic lattice point problem in conjugacy classes
Open access status: An open access version is available from UCL Discovery
DOI: 10.1515/forum-2015-0102
Publisher version: http://dx.doi.org/10.1515/forum-2015-0102
Language: English
Additional information: Copyright © 2016 by Walter de Gruyter GmbH.
Keywords: Lattice points; hyperbolic space; geodesic arcs
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1477487
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