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。