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Lattice point counting in sectors of Hyperbolic 3-space
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- Laaksonen, Niko (author)
- KTH,Matematik (Inst.)
- KTH Matematik (Inst) (creator_code:org_t)
- 2017-02-27
- 2017
- English.
- In: Quarterly Journal of Mathematics. - : Oxford University Press. - 0033-5606 .- 1464-3847. ; 68:3, s. 891-922
- Journal article (peer-reviewed)
Abstract
Subject headings
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- Let G be a cocompact discrete subgroup of PSL2(.) and denote by. the three-dimensional upper half-space. For a p I., we count the number of points in the orbit Gp, according to their distance, arccosh X, from a totally geodesic hyperplane. The main term in n dimensions was obtained by Herrmann for any subset of a totally geodesic submanifold. We prove a pointwise error term ofO(X3 2) by extending the method of Huber and Chatzakos-Petridis to three dimensions. By applying Chamizo's large sieve inequalities, we obtain the conjectured error term O(X1+ e) on an average in the spatial aspect. We prove a corresponding large sieve inequality for the radial average and explain why it only improves on the pointwise bound by 1/ 6.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Riemann Surfaces
- Large Sieve
- Plane
Publication and Content Type
- ref (subject category)
- art (subject category)
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