Avoiding algebraic integers of bounded house in orbits of rational functions over cyclotomic closures

Evan Chen

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…