论文标题
关于有限场上某些对角线方程的同时解决方案的数量
On the number of simultaneous solutions of certain diagonal equations over finite fields
论文作者
论文摘要
在本文中，我们获得了明确的估计和存在结果，这些结果是$ \ mathbb {f} _q $ - 合理解决方案的某些系统的数量，这些解决方案由对角方程的家族定义的有限字段定义。我们的方法依赖于对所涉及系统定义的品种的几何特性的研究。我们将这些结果应用于Waring问题的概括以及Modulo A属于质量数字的解决方案的分布。
In this paper we obtain explicit estimates and existence results on the number of $\mathbb{F}_q$-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.
