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

Authors  
Keywords  Mathematics 
Issue Date  1999 
Publisher  American Mathematical Society. 
Citation  Transactions of the American Mathematical Society, 1999, v. 352 n. 3, p. 10711111 How to Cite? 
Abstract  In 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 ErdösTurán 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 ErdösTurán 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 Identifier  http://hdl.handle.net/10722/48398 
ISSN  2015 Impact Factor: 1.196 2015 SCImago Journal Rankings: 2.168 
DC Field  Value  Language 

dc.contributor.author  Choi, KKS  en_HK 
dc.date.accessioned  20080522T04:11:40Z   
dc.date.available  20080522T04:11:40Z   
dc.date.issued  1999  en_HK 
dc.identifier.citation  Transactions of the American Mathematical Society, 1999, v. 352 n. 3, p. 10711111  en_HK 
dc.identifier.issn  00029947  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/48398   
dc.description.abstract  In 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 ErdösTurán 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 ErdösTurán 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.extent  1093674 bytes   
dc.format.extent  2143 bytes   
dc.format.mimetype  application/pdf   
dc.format.mimetype  text/plain   
dc.language  eng  en_HK 
dc.publisher  American Mathematical Society.  en_HK 
dc.rights  Transactions of the American Mathematical Society. Copyright © American Mathematical Society.  en_HK 
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.rights  First published in Transactions of the American Mathematical Society, 1999, v. 352 n. 3, p. 10711111, published by the American Mathematical Society,  en_HK 
dc.subject  Mathematics  en_HK 
dc.title  On the distribution of points in projective space of bounded height  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=00029947&volume=352&issue=3&spage=1071&epage=1111&date=1999&atitle=On+the+distribution+of+points+in+projective+space+of+bounded+height  en_HK 
dc.identifier.email  Choi, KKS: choi@maths.hku.hk  en_HK 
dc.description.nature  published_or_final_version  en_HK 
dc.identifier.scopus  eid_2s2.022844453744   