On the successive derived sets of the Pisot numbers
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- by David W. Boyd PDF
- Proc. Amer. Math. Soc. 73 (1979), 154-156 Request permission
Abstract:
Let S denote the set of Pisot (or Pisot-Vijayaraghavan) numbers and let ${S^{(k)}}$ be the kth derived set of S. It is shown that ${k^{1/2}} \leqslant \min {S^{(k)}}$ and that $\lim \sup (\min {S^{(k)}}/k) < 1$. The lower bound improves the estimate ${k^{1/4}} \leqslant \min {S^{(k)}}$ of Dufresnoy and Pisot, while the upper bound improves the obvious estimate $\min {S^{(k)}} \leqslant k + 1$.References
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D. W. Boyd, Pisot numbers and the width of meromorphic functions (privately circulated manuscript).
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 154-156
- MSC: Primary 12A15
- DOI: https://doi.org/10.1090/S0002-9939-1979-0516454-5
- MathSciNet review: 516454