PALINDROMIC RANDOM TRIGONOMETRIC POLYNOMIALS

被引：0

作者：

Conrey, J. Brian ^{[1
]}

Farmer, David W. ^{[1
]}

Imamoglu, Oezlem ^{[2
]}

机构：

[1] Amer Inst Math, Dept Math, Palo Alto, CA 94306 USA

[2] Eidgen Tech Hsch, Dept Math, CH-8092 Zurich, Switzerland

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 05期

基金：

美国国家科学基金会;

关键词：

ZEROS; REAL;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that if a real trigonometric polynomial has few real roots, then the trigonometric polynomial obtained by writing the coefficients in reverse order must have many real roots. This is used to show that, a class of random trigonometric polynomials has, on average, many real roots. In the case that the coefficients of a real trigonometric polynomial are independently and identically distributed, but with no other assumptions oil the distribution, the expected fraction of real zeros is at least one-half. This result is best possible.

引用

页码：1835 / 1839

页数：5

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