论文标题
Burgess在表格II：混合情况下评估的短字符总和的界限
Burgess bounds for short character sums evaluated at forms II: the mixed case
论文作者
论文摘要
这项工作证明了一个以$ n $尺寸为单位的简短混合字符总和的汉堡。可以在任何“可允许”形式中评估Prime导体$ Q $的非主要乘法特征，并且可以在任何实数的多项式中评估添加剂。当每个坐标中的总和至少为$β> 1/2-1/（2（n+1））$时，混合字符总和至少为$ q^β$时，所得的上限是不平凡的。这项工作利用了由于XU引起的乘法总和的最新分层，以及在任意维度中的vinogradov平均值定理的分辨率。
This work proves a Burgess bound for short mixed character sums in $n$ dimensions. The non-principal multiplicative character of prime conductor $q$ may be evaluated at any "admissible" form, and the additive character may be evaluated at any real-valued polynomial. The resulting upper bound for the mixed character sum is nontrivial when the length of the sum is at least $q^β$ with $β> 1/2 - 1/(2(n+1))$ in each coordinate. This work capitalizes on the recent stratification of multiplicative character sums due to Xu, and the resolution of the Vinogradov Mean Value Theorem in arbitrary dimensions.
