论文标题
在角色总和上
On character sums with determinants
论文作者
论文摘要
我们估计具有限制因素$ ad-bc $ $ 2 \ times 2 $矩阵模式的加权字符总和，带有条目$ a，b，c，d $在间隔$ [1，n] $上变化的条目。我们的目标是获得尽可能小的$ n $值的非平凡界限。特别是，我们以节省的能源实现了这个目标，以$ n \ ge p^{1/8+\ varepsilon} \ $使用任何固定的$ \ varepsilon> 0 $，除非有改善著名的伯吉斯绑定，否则这很可能是最好的。通过其他技术，我们还可以对待更多的一般总和，但有时以$ n $的较大值。
We estimate weighted character sums with determinants $ad-bc $ of $2\times 2$ matrices modulo a prime $p$ with entries $a,b,c,d $ varying over the interval $ [1,N]$. Our goal is to obtain nontrivial bounds for values of $N$ as small as possible. In particular, we achieve this goal, with a power saving, for $N \ge p^{1/8+\varepsilon}\ $ with any fixed $\varepsilon>0$, which is very likely to be the best possible unless the celebrated Burgess bound is improved. By other techniques, we also treat more general sums but sometimes for larger values of $N$.
