论文标题
单基期方程是环形多项式
Monogenic period equations are cyclotomic polynomials
论文作者
论文摘要
我们在{\ sl ofere equations}，$ψ_e（x）$中研究单差，高斯引入的辅助方程是通过自由基求解环形多项式的。所有单基因$ψ_e（x）$ getrees $ 4 \ leq e \ leq 250 $用于延长间隔$ p = ef+1 $，并与环形多种方案或简单的de moiv降低了环细胞元素的形式相吻合。以$ p = e+1 $而发生前一种情况，而后者则以$ p = 2e+1 $进行。对于$ e \ geq4 $，我们认为所有单基时期方程式为循环多项式。完全真实的时期方程在二次离散时间动态系统的应用中引起了人们的关注。
We study monogeneity in {\sl period equations}, $ψ_e(x)$, the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic $ψ_e(x)$ of degrees $4 \leq e \leq 250$ are determined for extended intervals of primes $p=ef+1$, and found to coincide either with cyclotomic polynomials, or with simple de Moivre reduced forms of cyclotomic polynomials. The former case occurs for $p=e+1$, and the latter for $p=2e+1$. For $e\geq4$, we conjecture all monogenic period equations to be cyclotomic polynomials. Totally real period equations are of interest in applications of quadratic discrete-time dynamical systems.
