报告名称：The number of rational points of a family of hypersurfaces over finite fields

报告专家：洪绍方

专家单位：四川大学网络空间安全学院

报告时间：12月18日10：00

报告地点：数统楼二楼会议室

专家简介：四川大学网络空间安全学院教授、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，多次访问美国、法国、日本，以色列、韩国以及香港和台湾等地区著名高校和研究所。于2013年参加在台湾大学举行的世界华人数学家大会，并作45分钟邀请报告。已经在国内外数学期刊发表学术论文百余篇，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。

报告摘要：Let F_q denote the finite field of odd characteristic p with q elements (q=p^{e},e\in \mathbb{N} ) and F_q^* represent the nonzero elements of F_q. In this paper, 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 F_q:\sum\limits_{j=0}^{t-1}\sum\limits_{i=1}^{r_{j+1}-r_j}a_{r_j+i}x_^{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 F_q, a_i\in 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.