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The hyperbolic lattice point problem in conjugacy classes

  • Dimitrios Chatzakos und Yiannis N. Petridis EMAIL logo
Veröffentlicht/Copyright: 10. Januar 2016

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\ 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.

MSC 2010: 11F72; 37C35; 37D40

Communicated by Jan Bruinier


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

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Received: 2015-5-28
Revised: 2015-11-4
Published Online: 2016-1-10
Published in Print: 2016-9-1

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