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Mathematics of Computation

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Orbits of algebraic numbers with low heights

Author: Gregory P. Dresden
Journal: Math. Comp. 67 (1998), 815-820
MSC (1991): Primary 11R04, 11R06; Secondary 12D10
MathSciNet review: 1468942
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Abstract: We prove that the two smallest values of $h(\alpha ) + h(\frac {1}{1-\alpha }) + h(1 - \frac {1}{\alpha })$ are $0$ and $0.4218\dots$, for $\alpha$ any algebraic integer.

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Additional Information

Gregory P. Dresden
Affiliation: Department of Mathematics, Washington & Lee University, Lexington, Virginia 24450

Received by editor(s): September 30, 1996
Additional Notes: I am very grateful for the assistance and guidance of my advisor, Dr. Vaaler.
Article copyright: © Copyright 1998 American Mathematical Society