论文标题
角色总和有限字段的稀疏元素
Character sums over sparse elements of finite fields
论文作者
论文摘要
我们估计多项式值的混合字符总和比有限字段的元素$ \ mathbb f_ {q^r} $在子场$ \ mathbb f_q $上以固定有序的基础上的固定有序表示。首先，我们将包含 - 排斥原理的组合与线性子空间上的字符总和上的界限相结合，以获得大型$ Q $的非平凡界限。然后，我们专注于特定情况$ q = 2 $，这更复杂。界限取决于某些自然限制。我们还提供了范围条件的示例家庭。特别是，我们将所有单元完全分类为我们界限适用的加性特征的参数。此外，我们还表明，它适用于包括所有倒数单元的大型理性功能。
We estimate mixed character sums of polynomial values over elements of a finite field $\mathbb F_{q^r}$ with sparse representations in a fixed ordered basis over the subfield $\mathbb F_q$. First we use a combination of the inclusion-exclusion principle with bounds on character sums over linear subspaces to get nontrivial bounds for large $q$. Then we focus on the particular case $q=2$, which is more intricate. The bounds depend on certain natural restrictions. We also provide families of examples for which the conditions of our bounds are fulfilled. In particular, we completely classify all monomials as argument of the additive character for which our bound is applicable. Moreover, we also show that it is applicable for a large family of rational functions, which includes all reciprocal monomials.
