Conjugates of Pisot numbers. (English) Zbl 1489.11108
In this paper the authors study the Galois conjugates of Pisot numbers. The main focus of this paper is a conjecture which states that if \(q\) is a Pisot number and \(q\in(1,2)\), then any Galois conjugate of \(q\) satisfies \(|q'|\geq \frac{\sqrt{5}-1}{2}\). Similar conjectures are made for \(q\in(m,m+1)\) for \(m\geq 2\). The authors provide evidence of a theoretical and computational nature which supports the validity of these conjectures. Last of all, the authors relate this conjecture to the dimension of Bernoulli convolutions parameterised by the reciprocal of a Pisot number.
Reviewer: Simon Baker (Birmingham)
MSC:
| 11K16 | Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. |
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