论文标题
在乘法倒置下关闭的无汇总集
Sum-free sets which are closed under multiplicative inverses
论文作者
论文摘要
令$ a $为有限字段$ \ mathbb {f} $的子集。当$ \ mathbb {f} $具有质量订单时，我们表明有一个绝对常数$ c> 0 $，因此，如果$ a $既是无价值且等于其乘数倒置的集合，又等于$ | a | <（0.25 -c）| \ mathbb {f} | + o（| \ mathbb {f} |）$ as $ | | \ Mathbb {f} | \ rightarrow \ infty $。我们将其与至少$ 0.25 | \ mathbb {f} |存在的结果形成鲜明对比。 - o（| \ mathbb {f} |）$当$ \ mathbb {f} $具有特征$ 2 $时。
Let $A$ be a subset of a finite field $\mathbb{F}$. When $\mathbb{F}$ has prime order, we show that there is an absolute constant $c > 0$ such that, if $A$ is both sum-free and equal to the set of its multiplicative inverses, then $|A| < (0.25 - c)|\mathbb{F}| + o(|\mathbb{F}|)$ as $|\mathbb{F}| \rightarrow \infty$. We contrast this with the result that such sets exist with size at least $0.25|\mathbb{F}| - o(|\mathbb{F}|)$ when $\mathbb{F}$ has characteristic $2$.
