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.
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页码：1835 / 1839
页数：5
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