随机多项式的实零点，I：翻转不变性，图兰引理和牛顿-阿达玛多边形
Real zeroes of random polynomials, I: Flip-invariance, Turán's lemma, and the Newton-Hadamard polygon
摘要：
我们表明，具有很高的概率，一个随机多项式的实零点的数量是有界的牛顿-阿达玛多边形乘以多项式次数的对数的立方的顶点数。类似的估计适用于复平面中任何曲线上的零，复平面是极坐标中Lipschitz函数的图形。证明是基于经典的图兰引理。
英文摘要：
We show that with high probability the number of real zeroes of a random polynomial is bounded by the number of vertices on its Newton-Hadamard polygon times the cube of the logarithm of the polynomial degree. A similar estimate holds for zeroes lying on any curve in the complex plane, which is the graph of a Lipschitz function in polar coordinates. The proof is based on the classical Turán lemma.
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。
