论文标题
多项式具有许多合理的前牙科点
Polynomials with many rational preperiodic points
论文作者
论文摘要
在本文中，我们研究了两个问题与$ \ mathbb {q} [x] $中多项式前点的特殊行为有关。我们表明，对于所有$ d \ geq 2 $，存在一个多项式$ f_d（x）\ in \ mathbb {q} [x] [x] $，$ 2 \ leq \ leq \ mathrm {deg}（f_d）（f_d）\ leq d $ to $ f_d（x）$至少具有$ d + d + lflo \ lflo \ log \ lflo \ lflo \ rlo \ r。点。此外，我们表明，对于无限的许多整数$ d $，polyenmials $ f_d（x）$和$ f_d（x） + 1 $至少具有$ d^2 + d \ d \ lfloor \ log_2（d）\ rfloor -2d + 1d + 1 dd + 1 $ commun complect postery posteriodic pote。
In this paper we study two questions related to exceptional behavior of preperiodic points of polynomials in $\mathbb{Q}[x]$. We show that for all $d\geq 2$, there exists a polynomial $f_d(x) \in \mathbb{Q}[x]$ with $2\leq \mathrm{deg}(f_d) \leq d$ such that $f_d(x)$ has at least $d + \lfloor \log_2(d)\rfloor$ rational preperiodic points. Furthermore, we show that for infinitely many integers $d$, the polynomials $f_d(x)$ and $f_d(x) + 1$ have at least $d^2 + d\lfloor \log_2(d)\rfloor - 2d + 1$ common complex preperiodic points.
