论文标题
残基类别和不可约多项式的生成器中无方的平滑多项式
Square-free smooth polynomials in residue classes and generators of irreducible polynomials
论文作者
论文摘要
在A. Booker and C. Pomerance（2017）的基础上，我们证明，对于Prime Power $ Q \ geq 7 $，每个残留类别模式都不可及的多项式$ f \ in \ Mathbb {f} _q [x] $具有非稳定的，无依赖的代表性的$ few –1 $ few –1 $ f in \ mathbb {f} _q [x] $ n \ mathbb {f} _q [x] $ a i;我们还将应用于生成不可约多项式的序列。
Building upon the work of A. Booker and C. Pomerance (2017), we prove that for a prime power $q \geq 7$, every residue class modulo an irreducible polynomial $F \in \mathbb{F}_q[X]$ has a non-constant, square-free representative which has no irreducible factors of degree exceeding $\text{deg}~F -1$. We also give applications to generating sequences of irreducible polynomials.
