| 有限域上由两个广义对角多项式所确定的簇中的有理点 |
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| 引用本文： | 李涛,谭千蓉. 有限域上由两个广义对角多项式所确定的簇中的有理点[J]. 四川大学学报(自然科学版), 2009, 46(6): 1592-1594. DOI: 10.3969/j.issn.0490-6756.2009.06.004 |
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| 作者姓名： | 李涛 谭千蓉 |
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| 作者单位： | 四川大学数学学院,成都,610064,;攀枝花学院计算机学院,攀枝花,617000 |
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| 摘 要： | 设Fq为有限域,f_l=a_(l1)x(~d~(l)_(11))_(11)…x~(d~((l))_(1_(k1)))_(1_(k1))+a_(l2)x~(d~((l))_(21))_(21)…x~(d~((l))_(2k_2)_(2k_2))+…+a_(ln)x~(d~((l))_(n1))_(n1)…x~(d~((l))_(nk_n)_(nk_n)+c_l(l=1,2)为F_q上的一组广义对角多项式,用N_q(V)表示由f_l(l=1,2)确定的族中的F_q有理点的个数.作者利用Adolphson和Sperber的牛顿多面体理论与指数和工具,证明了ord_qN_q(V)≥max{「∑~n_(i=1)1/d_i」-2,0,其中d_i=max{d~(1)_(ij),d~(2)_(ij)|1≤j≤k_i},1≤i≤n.
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| 关 键 词： | 广义对角多项式组 有理点个数 有限域 |
| 收稿时间： | 2008-04-02 |
Rational points on the variety defined by two generalized diagonal polynomials over finite field |
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| LI Tao and TAN Qian-Rong. Rational points on the variety defined by two generalized diagonal polynomials over finite field[J]. Journal of Sichuan University (Natural Science Edition), 2009, 46(6): 1592-1594. DOI: 10.3969/j.issn.0490-6756.2009.06.004 |
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| Authors: | LI Tao and TAN Qian-Rong |
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| Affiliation: | School of Mathematics, Sichuan University;School of Computer Science and Technology, Panzhihua University |
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| Abstract: | Let F_q be the finite field and N_q(V) denote the number of F_q rational points on the variety determined by f_l=a_(l1)x(~d~(l)_(11))_(11)…x~(d~((l))_(1_(k1)))_(1_(k1))+a_(l2)x~(d~((l))_(21))_(21)…x~(d~((l))_(2k_2)_(2k_2))+…+a_(ln)x~(d~((l))_(n1))_(n1)…x~(d~((l))_(nk_n)_(nk_n)+c_l(l=1,2)By using the Newton polyhedra technique introduced by Adolphson and Sperber, the authors prove that ord_qN_q(V)≥max{「∑~n_(i=1)1/d_i」-2,0,where d_i=max{d~((1))_(ij),d~((2))_(ij)|1≤j≤k_i},1≤i≤n. |
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| Keywords: | generalized diagonal polynomial number of rational points finite field |
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