论文标题
单一政治多项式的统一交叉点不可能
Uniform unlikely intersections for unicritical polynomials
论文作者
论文摘要
修复$ d \ geq2 $，让$ f_ {t}（z）= z^{d}+t $是由$ t \ in \ mathbb {c} $参数化的多项式的家族。在本文中，我们将证明存在一个常数$ c（d）$，以便对于任何$ a，b \ in \ mathbb {c} $，带有$ a^{d} \ neq b^{d} $，$ t \ in \ mathbb {c}的$ t \ in \ mathbb {c} $ a $ a $ a $和$ b $ a $ ins $ iS $ f_ at $ f_ a $ f_ a $ c $ c）
Fix $d\geq2$ and let $f_{t}(z)=z^{d}+t$ be the family 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 $C(d)$.
