報告名稱：The number of rational points of a family of hypersurfaces over finite fields

報告專家：洪紹方

專家單位：四川大學yl7703永利

報告時間：12月18日10：00

報告地點：數統樓二樓會議室

專家簡介：四川大學yl7703永利教授、博士生導師、教育部新世紀優秀人才、四川省學術與技術帶頭人，多次訪問美國、法國、日本，以色列、韓國以及香港和台灣等地區著名高校和研究所。于2013年參加在台灣大學舉行的世界華人數學家大會，并作45分鐘邀請報告。已經在國内外數學期刊發表學術論文百餘篇，培養畢業碩士60多名、畢業博士20 多名，其中多人已晉升正高職稱。

報告摘要：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.