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arXiv · 2009.12251

Uniform unlikely intersections for unicritical polynomials

Hang Fu
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Abstract

Fix $d\geq2$, and consider the family $f_{t}(z)=z^{d}+t$ of polynomials parameterized by $t\in\mathbb{C}$. In this article, we will show that there exists a constant $C(d)$ such that for any $a,b\in\mathbb{C}$ with $a^{d}\neq b^{d}$, the number of $t\in\mathbb{C}$ such that $a$ and $b$ are both preperiodic for $f_{t}$ is at most $C(d)$.

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Hang Fu. 2020-09-25. Uniform unlikely intersections for unicritical polynomials. https://doi.org/10.46298/epiga.2026.10958

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