论文标题
多项式真实和独特的根部是什么时候？图形视图
When are the roots of a polynomial real and distinct? A graphical view
论文作者
论文摘要
我们证明了至少可以追溯到傅立叶的经典结果，即具有真实系数的多项式在且仅当多项式及其所有非恒定衍生物都只有负的minima和阳性最大值时，具有真实和独特的所有零。详细描述了涉及照明图片的结果的直觉。将傅立叶定理的推广到某些阶命令的整个功能（猜想）表明，对Riemann假设千年问题的官方描述错误地描述了与Riemann假设的等效性。该论文是相当独立的，并且可以为参加两个学期的微积分的学生提供（可能有一些帮助）。
We prove the classical result, which goes back at least to Fourier, that a polynomial with real coefficients has all zeros real and distinct if and only if the polynomial and also all of its nonconstant derivatives have only negative minima and positive maxima. Intuition for the result, involving illuminating pictures, is described in detail. The generalization of Fourier's theorem to certain entire functions of order one (which is conjectural) suggests that the official description of the Riemann Hypothesis Millennium Problem incorrectly describes an equivalence to the Riemann Hypothesis. The paper is reasonably self-contained and is intended be accessible (possibly with some help) to students who have taken two semesters of calculus.
