Sums of heights of algebraic numbers
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- by Gregory P. Dresden PDF
- Math. Comp. 72 (2003), 1487-1499 Request permission
Abstract:
For $A_t(x) = f(x) - t g(x)$, we consider the set $\{ \sum _{A_t(\alpha ) = 0} h(\alpha ) : t \in \overline {\mathbb {Q}} \}$. The polynomials $f(x), g(x)$ are in $\mathbb {Z}[x]$, with only mild restrictions, and $h(\alpha )$ is the Weil height of $\alpha$. We show that this set is dense in $[d, \infty )$ for some effectively computable limit point $d$.References
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Additional Information
- Gregory P. Dresden
- Affiliation: Department of Mathematics, Washington & Lee University, Lexington, Virginia 24450-0303
- Email: dresdeng@wlu.edu
- Received by editor(s): May 24, 1999
- Received by editor(s) in revised form: December 10, 2001
- Published electronically: December 6, 2002
- Additional Notes: I would like to thank Dr. C. J. Smyth and Dr. J. Vaaler, and I would also like to thank the referee for helpful comments and an improved proof of Theorem 6.1.
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1487-1499
- MSC (2000): Primary 11R04, 11R06; Secondary 12D10
- DOI: https://doi.org/10.1090/S0025-5718-02-01481-3
- MathSciNet review: 1972748