学术报告

题      目：The number of rational points of a family of hypersurfaces over finite fields

报  告  人：洪绍方  教授  (邀请人：袁平之 )

                                    四川大学

时      间：11月02日  11：00-12：00

地     点：数科院东楼401报告厅

报告人简介:

        洪绍方，四川大学数学学院教授、博士生导师，教育部新世纪优秀人才，四川省学术与技术带头人。已经在国内外数学期刊发表学术论文一百多篇，培养毕业硕士60多名，毕业博士20 多名，其中多人已晋升正高职称。

摘      要：

       In this talk, by using the Smith normal form of the index matrix, we give a formula for the number of rational points of the following family of hypersurface over $\mathbb{F}_q$:$$\sum\limits_{j=0}^{t-1}\sum\limits_{i=1}^{r_{j+1}-r_j}a_{r_j+i}x_1^{e_{r_j+i,1}} ...x_{n_{j+1}}^{e_{r_j+i,n_{j+1}}}-b=0,$$where the integers $t>0$, $r_0=0<r_1<r_2< ...<r_t$, $n_1< n_2< ...<n_t$, $b\in \mathbb{F}_q$, $a_i\in \mathbb{F}_q^*$ $(i=1,...,r_t)$,and the index of each variable is a positive integer. Especially under some certain conditions, we get an explicit formula of the number of rational points of the above hypersurface. This generalizes greatly the results obtained by Wolfmann in 1994, Sun in 1997 and
Wang and Sun in 2005, respectively. 

         欢迎所有相关方向老师和研究生参加。