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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Orbits of algebraic numbers with low heights
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by Gregory P. Dresden PDF
Math. Comp. 67 (1998), 815-820 Request permission


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
  • Email:
  • Received by editor(s): September 30, 1996
  • Additional Notes: I am very grateful for the assistance and guidance of my advisor, Dr. Vaaler.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 815-820
  • MSC (1991): Primary 11R04, 11R06; Secondary 12D10
  • DOI:
  • MathSciNet review: 1468942