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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Counting primitive points of bounded height


Author: Martin Widmer
Journal: Trans. Amer. Math. Soc. 362 (2010), 4793-4829
MSC (2010): Primary 11G35; Secondary 11D75, 11G50, 14G25
Published electronically: April 28, 2010
MathSciNet review: 2645051
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Abstract: Let $ k$ be a number field and $ K$ a finite extension of $ k$. We count points of bounded height in projective space over the field $ K$ generating the extension $ K/k$. As the height gets large we derive asymptotic estimates with a particularly good error term respecting the extension $ K/k$. In a future paper we will use these results to get asymptotic estimates for the number of points of fixed degree over $ k$. We also introduce the notion of an adelic Lipschitz height generalizing that of Masser and Vaaler. This will lead to further applications involving points of fixed degree on linear varieties and algebraic numbers of fixed degree satisfying certain subfield conditions.


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Additional Information

Martin Widmer
Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
Address at time of publication: Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712
Email: widmer@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05173-1
PII: S 0002-9947(10)05173-1
Received by editor(s): November 25, 2008
Published electronically: April 28, 2010
Additional Notes: The author was supported by NSF Grant #118647
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.