论文标题
限制可变的雪瓦利修饰定理
Restricted Variable Chevalley-Warning Theorems
论文作者
论文摘要
我们在有限领域的低度多项式系统中追求雪佛兰修饰定理的各种限制可变概括。我们的第一个结果涉及限于Gács-Weiner和Sziklai-Takáts定义的$ \ f_q $ vandermonde子集的笛卡尔产品。然后，我们定义了$ \ f_q^n $的非空子集的不变$ \ uomega（x）$。我们的第二个结果涉及$ x $限制的变量，当多项式的学位与$ \ uomega（x）$相比。最后，我们探索了$ \ uomega（x）$可以从下面界定的各种类别的子集。
We pursue various restricted variable generalizations of the Chevalley-Warning theorem for low degree polynomial systems over a finite field. Our first such result involves variables restricted to Cartesian products of the Vandermonde subsets of $\F_q$ defined by Gács-Weiner and Sziklai-Takáts. We then define an invariant $\uomega(X)$ of a nonempty subset of $\F_q^n$. Our second result involves $X$-restricted variables when the degrees of the polynomials are small compared to $\uomega(X)$. We end by exploring various classes of subsets for which $\uomega(X)$ can be bounded from below.
