论文标题
$ l $ - 功能和总组合
$L$--functions and sum--free sets
论文作者
论文摘要
对于集合$ a \ subset {\ mathbb {f} _p}^*$ by $ {\ Mathsf {\ Mathsf {sf}}（a）$最大总的$ A的大小 - $A。$A。如果$ {\ mathsf {sf}}（a） - | a |/3 $很小，则集合$ a $必须均匀地分布在每个大型乘法子组的cosets上。我们的参数依赖于在$ {\ mathbb {f} _p} $中在某些间隔上分布的不规则性。
For set $A\subset {\mathbb {F}_p}^*$ define by ${\mathsf{sf}}(A)$ the size of the largest sum--free subset of $A.$ Alon and Kleitman showed that ${\mathsf{sf}} (A) \ge |A|/3+O(|A|/p).$ We prove that if ${\mathsf{sf}} (A)-|A|/3$ is small then the set $A$ must be uniformly distributed on cosets of each large multiplicative subgroup. Our argument relies on irregularity of distribution of multiplicative subgroups on certain intervals in ${\mathbb {F}_p}$.
