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Forum Mathematicum

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Volume 28, Issue 5


The hyperbolic lattice point problem in conjugacy classes

Dimitrios Chatzakos
  • Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom of Great Britain and Northern Ireland
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/ Yiannis N. Petridis
  • Corresponding author
  • Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom of Great Britain and Northern Ireland
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Published Online: 2016-01-10 | DOI: https://doi.org/10.1515/forum-2015-0102


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\ 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() we interpret our results in terms of indefinite quadratic forms.

Keywords: Lattice points; hyperbolic space; geodesic arcs

MSC 2010: 11F72; 37C35; 37D40


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About the article

Received: 2015-05-28

Revised: 2015-11-04

Published Online: 2016-01-10

Published in Print: 2016-09-01

The first author was supported by a DTA from EPSRC during his PhD studies at UCL.

Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 981–1003, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0102.

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