Density of Unicritical Polynomials over Local Fields with Rational Periodic Points
We prove an asymptotic formula for the density of parameters $c\in \mathbb{Z}_p$ for which the polynomial $x^d+c$ admits a $\mathbb{Q}_p$-rational $n$-cycle. In the cases where $d=2$ and $p\neq 2,3$, we compute these densities explicitly for $n=1,2,$ and $3$.
math.NT↗