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Dynamical uniform boundedness for unicritical polynomials
We prove the dynamical uniform boundedness conjecture for unicritical polynomials $z^d + c$ over every number field $K$ when $d \geq 4$, and over every number field $K$ not containing $\mathbb{Q}(\sqrt{-3})$ when $d = 3$. Furthermore, our unconditional bounds on perodic points are effectively comput
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