Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Lattice point counting in sectors of Hyperbolic 3-space
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Quarterly Journal of Mathematics, ISSN 0033-5606, E-ISSN 1464-3847, Vol. 68, no 3, p. 891-922Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Oxford University Press, 2017. Vol. 68, no 3, p. 891-922
Keywords [en]
Riemann Surfaces, Large Sieve, Plane
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215375DOI: 10.1093/qmath/hax004ISI: 000410659500010Scopus ID: 2-s2.0-85029783701OAI: oai:DiVA.org:kth-215375DiVA, id: diva2:1148181
Note

QC 20171010

Available from: 2017-10-10 Created: 2017-10-10 Last updated: 2017-10-10Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Laaksonen, Niko
By organisation
Mathematics (Dept.)
In the same journal
Quarterly Journal of Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 4 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf