论文标题
$ \ mathbb {z} $上的本地nilpotent多项式
Locally nilpotent polynomials over $\mathbb{Z}$
论文作者
论文摘要
对于多项式$ u（x）$ in $ \ mathbb {z} [x] $和$ r \ in \ mathbb {z} $，我们考虑$ u（x）$ at $ r $，$ r $，$ r $，$ \ mathcal {o} _u} _u（o} _u（r）（r）的轨道：我们在这里提出两个问题：（i）多项式$ u $是$ 0 \ in \ Mathcal {o} _u（r）$和（ii）多项式的多项式是什么，哪些$ 0 \ in \ in \ not \ mathcal {o} _u（o} _U（r）_u（r）$ p $ p $ p $ p $ p $ 0}在本文中，我们对（ii）所保留的多项式进行了分类。我们还为某些特殊的$ r'$ s提供了一些结果，可以回答（i）。
For a polynomial $u(x)$ in $\mathbb{Z}[x]$ and $r\in\mathbb{Z}$, we consider the orbit of $u(x)$ at $r$, $\mathcal{O}_u(r):=\{u(r),u(u(r)),\ldots\}$. We ask two questions here: (i) what are the polynomials $u$ for which $0\in \mathcal{O}_u(r)$ and (ii) what are the polynomials for which $0\not\in \mathcal{O}_u(r)$ but, modulo every prime $p$, $0\in \mathcal{O}_u(r)$? In this paper we classify the polynomials for which (ii) holds. We also present some results for some special $r'$s for which (i) can be answered.
