根均在单位圆上的共轭互反多项式
Conjugate Reciprocal Polynomials with all Roots on the Unit Circle
摘要：
本文研究了根均在单位圆上的固定次数一次共轭互反多项式集的几何、拓扑和勒贝格测度。这样的N次多项式的集合自然地与$\R^{N-1}$的子集相关联。我们计算了该集合的体积，证明了该集合与$N-1$球同胚，其等距群与$2N$阶二面体群同构.
英文摘要：
We study the geometry, topology and Lebesgue measure of the set of monic conjugate reciprocal polynomials of fixed degree with all roots on the unit circle. The set of such polynomials of degree N is naturally associated to a subset of $\R^{N-1}$. We calculate the volume of this set, prove the set is homeomorphic to the $N-1$ ball and that its isometry group is isomorphic to the dihedral group of order $2N$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
