论文标题
在某些结构化集和应用程序上的添加双字符总和
Additive double character sums over some structured sets and applications
论文作者
论文摘要
我们研究了有限场的两个子集的加性双字符总和。我们表明，如果有一个适当的理性自图集合的集合$ d $，那么该集合包含一个大子集$ u $，标准限制了$ u $上的字符总和和任何子集$ c $的绝对值（可以满足其尺寸$ | c | $的任何限制）。这种合适的自图的例子是反转和平方。然后，我们将这种新绑定应用于追踪产品和总产品方程，并改善第一作者和Gyarmati和Sárközy的结果。
We study additive double character sums over two subsets of a finite field. We show that if there is a suitable rational self-map of small degree of a set $D$, then this set contains a large subset $U$ for which the standard bound on the absolute value of the character sum over $U$ and any subset $C$ (which satisfies some restrictions on its size $|C|$) can be improved. Examples of such suitable self-maps are inversion and squaring. Then we apply this new bound to trace products and sum-product equations and improve results of the first author and of Gyarmati and Sárközy.
