少零点余弦多项式
Cosine polynomials with few zeros
摘要：
Borwein，Erdélyi，Ferguson和Lockhart在一篇著名的论文中构造了\[ f_A(x) = \sum_{a \in A} \cos(ax), \]形式的余弦多项式，其中$A\subseteq \mathbb{N}$，$|A|= n$和$[0,2π]$中只有$n^{5/6+o(1)}$零点，从而反驳了J.E.利特尔伍德在这里，我们给出了一个尖锐的分析，其结构，并作为一个结果，证明存在的例子，少至$C(n\log n)^{2/3}$根。
英文摘要：
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.
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。
