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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 algebraic numbers with large height II


Authors: David Masser and Jeffrey D. Vaaler
Journal: Trans. Amer. Math. Soc. 359 (2007), 427-445
MSC (2000): Primary 11R04
Published electronically: August 24, 2006
MathSciNet review: 2247898
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Abstract: We count algebraic numbers of fixed degree over a fixed algebraic number field. When the heights of the algebraic numbers are bounded above by a large parameter $ \mathcal{H}$, we obtain asymptotic estimates for their cardinality as $ \mathcal{H} \rightarrow \infty $.


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Additional Information

David Masser
Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
Email: David.Masser@unibas.ch

Jeffrey D. Vaaler
Affiliation: Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712
Email: vaaler@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04115-8
PII: S 0002-9947(06)04115-8
Keywords: Mahler measure, height
Received by editor(s): December 14, 2004
Published electronically: August 24, 2006
Additional Notes: The research of the second author was supported in part by the National Science Foundation (DMS-00-88915).
Article copyright: © Copyright 2006 American Mathematical Society