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| Main Author: | |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1608.04146 |
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Table of Contents:
- Let $k$ be a number field with cyclotomic closure $k^{\mathrm{cyc}}$, and let $h \in k^{\mathrm{cyc}}(x)$. For $A \ge 1$ a real number, we show that \[ \{ α\in k^{\mathrm{cyc}} : h(α) \in \overline{\mathbb Z} \text{ has house at most } A \} \] is finite for many $h$. We also show that for many such $h$ the same result holds if $h(α)$ is replaced by orbits $h(h(\cdots h(α)))$. This generalizes a result proved by Ostafe that concerns avoiding roots of unity, which is the case $A=1$.