论文标题
多项式的积分零，线性复发为系数
Integral zeros of a polynomial with linear recurrences as coefficients
论文作者
论文摘要
令$ k $为一个数字字段，$ s $是$ k $的有限位置，$ \ m rathcal {o} _s $是$ s $ -Integers的戒指。此外，让$$ g_n^{（0）} z^d + \ cdots + g_n^{（d-1）} z + g_n^{（d）} $ z $ z $中的多项式，具有简单的线性复发，对$ n $作为系数进行了评估的整数。假设有一些技术条件，我们给出了上述多项式的零$（n，z）\ in \ mathbb {n} \ times \ mathcal {o} _s $的描述。我们还以对这种多项式的希尔伯特不可约性精神的结果。
Let $ K $ be a number field, $ S $ a finite set of places of $ K $, and $ \mathcal{O}_S $ be the ring of $ S $-integers. Moreover, let $$ G_n^{(0)} Z^d + \cdots + G_n^{(d-1)} Z + G_n^{(d)} $$ be a polynomial in $ Z $ having simple linear recurrences of integers evaluated at $ n $ as coefficients. Assuming some technical conditions we give a description of the zeros $ (n,z) \in \mathbb{N} \times \mathcal{O}_S $ of the above polynomial. We also give a result in the spirit of Hilbert irreducibility for such polynomials.
