论文标题
余弦多项式，很少
Cosine polynomials with few zeros
论文作者
论文摘要
在一篇著名的论文中，Borwein，Erdélyi，Ferguson和Lockhart在A} \ cos（ax）中构建了形式\ [f_a（x）= \ sum_ {a \ in a} \ cos（ax），\]的余弦多项式，用$ $ [0,2π] $中的零，从而反驳了J.E. Littlewood的旧猜想。在这里，我们对它们的结构进行了彻底的分析，结果证明存在的示例少于$ c（n \ log n）^{2/3} $ roots。
In a celebrated paper, Borwein, Erdélyi, Ferguson and Lockhart constructed cosine polynomials of the form \[ f_A(x) = \sum_{a \in A} \cos(ax), \] with $A\subseteq \mathbb{N}$, $|A|= n$ and as few as $n^{5/6+o(1)}$ zeros in $[0,2π]$, thereby disproving an old conjecture of J.E. Littlewood. Here we give a sharp analysis of their constructions and, as a result, prove that there exist examples with as few as $C(n\log n)^{2/3}$ roots.
