Mathematics of Computation

Author(s): Gregory P. Dresden.
Journal: Math. Comp. 72 (2003), 1487-1499.
MSC (2000): Primary 11R04, 11R06; Secondary 12D10
Posted: December 6, 2002
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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

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

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Retrieve articles in Mathematics of Computation with MSC (2000): 11R04, 11R06, 12D10

Gregory P. Dresden
Affiliation: Department of Mathematics, Washington & Lee University, Lexington, Virginia 24450-0303
Email: dresdeng@wlu.edu

DOI: 10.1090/S0025-5718-02-01481-3
PII: S 0025-5718(02)01481-3
Received by editor(s): May 24, 1999
Received by editor(s) in revised form: December 10, 2001
Posted: 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 of article: Copyright 2002, American Mathematical Society

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