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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Counting primitive points of bounded height
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by Martin Widmer PDF
Trans. Amer. Math. Soc. 362 (2010), 4793-4829 Request permission


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:
  • Received by editor(s): November 25, 2008
  • Published electronically: April 28, 2010
  • Additional Notes: The author was supported by NSF Grant #118647
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 4793-4829
  • MSC (2010): Primary 11G35; Secondary 11D75, 11G50, 14G25
  • DOI:
  • MathSciNet review: 2645051