# 学术报告：2018年9月8日10:30-11:30，周海燕，南京师范大学

 报告人 周海燕 单位 南京师范大学 报告题目 Countingpoints on diagonal   equations over Galois rings GR$(p^{2},p^{2r})$ 报告时间 2018年9月8日 地点 东南大学数学学院第一报告厅 邀请人 卢伟 吴霞 报告摘要 Let $\F_q$ be the finite field with   $q=p^s$ elements, where $p$ is a prime and $s>1$ is an integer. A diagonal   equation over $\F_q$ is an equation of the form   $$a_1x_1^{k_1}+a_2x_2^{k_2}+\cdots+a_nx_n^{k_n}=b\eqno(1)$$with positive   integers $k_1,\ \cdots,\ k_n$, $a_1,\ \cdots,\ a_n\in\F_q^*$ and $b\in\F_q$.   The number of solutions $$N=N(a_1x_1^{k_1}+a_2x_2^{k_2}+\cdots+a_nx_n^{k_n}=b)$$   of $(1)$ in $\F_q^n$ can be expressed by Jacobi type sums, and the precise   number of solutions can be also be obtained when $k_1=k_2=\cdots=k_n=2$, but   in general some estimates can be satisfied. In this talk, we are interesting in   the number of solutions of diagonal equations over Galois rings. 报告人简介 周海燕，南京师范大学，教授，主要研究方向为代数数论、代数K理论以及有限域相关理论。