论文标题
关于脱骨多项式的分解
On the Factorization of lacunary polynomials
论文作者
论文摘要
本文解决了表格$ f（x）= f_ {0}（x） + f_ {1}（x）x^{n} + cdots + f_ {r-1}（x）x^{（r-1）n} + f_} + f_ {rn = a $ rn = a $ rn = rn $ rn $ rn和$ f_ {j}（x）$是$ \ mathbb z [x] $的固定多项式，对于$ 0 \ le J \ le r $。我们提供了一种有效的方法，可以表明$ f_ {j}（x）$的$ n $足够大且合理的条件，$ f（x）$的非重点部分是$ 1 $或不可避免的。我们说明了这种方法，包括给出两个示例，这些示例来自双曲线$ 3 $ manifolds的痕迹。
This paper addresses the factorization of polynomials of the form $F(x) = f_{0}(x) + f_{1}(x) x^{n} + \cdots + f_{r-1}(x) x^{(r-1)n} + f_{r}(x) x^{rn}$ where $r$ is a fixed positive integer and the $f_{j}(x)$ are fixed polynomials in $\mathbb Z[x]$ for $0 \le j \le r$. We provide an efficient method for showing that for $n$ sufficiently large and reasonable conditions on the $f_{j}(x)$, the non-reciprocal part of $F(x)$ is either $1$ or irreducible. We illustrate the approach including giving two examples that arise from trace fields of hyperbolic $3$-manifolds.
