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Article: On the distribution of points in projective space of bounded height

TitleOn the distribution of points in projective space of bounded height
Authors
KeywordsMathematics
Issue Date1999
PublisherAmerican Mathematical Society.
Citation
Transactions of the American Mathematical Society, 1999, v. 352 n. 3, p. 1071-1111 How to Cite?
AbstractIn this paper we consider the uniform distribution of points in compact metric spaces. We assume that there exists a probability measure on the Borel subsets of the space which is invariant under a suitable group of isometries. In this setting we prove the analogue of Weyl's criterion and the Erdös-Turán inequality by using orthogonal polynomials associated with the space and the measure. In particular, we discuss the special case of projective space over completions of number fields in some detail. An invariant measure in these projective spaces is introduced, and the explicit formulas for the orthogonal polynomials in this case are given. Finally, using the analogous Erdös-Turán inequality, we prove that the set of all projective points over the number field with bounded Arakelov height is uniformly distributed with respect to the invariant measure as the bound increases.
Persistent Identifierhttp://hdl.handle.net/10722/48398
ISSN
2015 Impact Factor: 1.196
2015 SCImago Journal Rankings: 2.168

 

DC FieldValueLanguage
dc.contributor.authorChoi, KKSen_HK
dc.date.accessioned2008-05-22T04:11:40Z-
dc.date.available2008-05-22T04:11:40Z-
dc.date.issued1999en_HK
dc.identifier.citationTransactions of the American Mathematical Society, 1999, v. 352 n. 3, p. 1071-1111en_HK
dc.identifier.issn0002-9947en_HK
dc.identifier.urihttp://hdl.handle.net/10722/48398-
dc.description.abstractIn this paper we consider the uniform distribution of points in compact metric spaces. We assume that there exists a probability measure on the Borel subsets of the space which is invariant under a suitable group of isometries. In this setting we prove the analogue of Weyl's criterion and the Erdös-Turán inequality by using orthogonal polynomials associated with the space and the measure. In particular, we discuss the special case of projective space over completions of number fields in some detail. An invariant measure in these projective spaces is introduced, and the explicit formulas for the orthogonal polynomials in this case are given. Finally, using the analogous Erdös-Turán inequality, we prove that the set of all projective points over the number field with bounded Arakelov height is uniformly distributed with respect to the invariant measure as the bound increases.en_HK
dc.format.extent1093674 bytes-
dc.format.extent2143 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAmerican Mathematical Society.en_HK
dc.rightsTransactions of the American Mathematical Society. Copyright © American Mathematical Society.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsFirst published in Transactions of the American Mathematical Society, 1999, v. 352 n. 3, p. 1071-1111, published by the American Mathematical Society,en_HK
dc.subjectMathematicsen_HK
dc.titleOn the distribution of points in projective space of bounded heighten_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0002-9947&volume=352&issue=3&spage=1071&epage=1111&date=1999&atitle=On+the+distribution+of+points+in+projective+space+of+bounded+heighten_HK
dc.identifier.emailChoi, KKS: choi@maths.hku.hken_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-22844453744-

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