Counting algebraic numbers with large height II
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- by David Masser and Jeffrey D. Vaaler PDF
- Trans. Amer. Math. Soc. 359 (2007), 427-445 Request permission
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 $\mathcal {H} \rightarrow \infty$.References
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Additional Information
- David Masser
- Affiliation: Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
- MR Author ID: 121080
- Email: David.Masser@unibas.ch
- Jeffrey D. Vaaler
- Affiliation: Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712
- MR Author ID: 176405
- Email: vaaler@math.utexas.edu
- 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).
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 427-445
- MSC (2000): Primary 11R04
- DOI: https://doi.org/10.1090/S0002-9947-06-04115-8
- MathSciNet review: 2247898