| 有限域上一类方程组解数的直接公式 |
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| 引用本文： | 杨继明.有限域上一类方程组解数的直接公式[J].数学学报,2007,50(3):653-660. |
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| 作者姓名： | 杨继明 |
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| 作者单位： | 玉溪师范学院数学系 玉溪 |
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| 基金项目： | 致谢 衷心感谢导师赵春来教授的指导和帮助!对审稿人提出的宝贵意见深表谢意! |
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| 摘 要： | 本文给出有限域F=F_q(q=p~f,f≥1,p是一个奇素数)上一类方程组∑_(i=s_(r-1)+1~(s_r)∑_(j=1)~(m_i-m_(i-1))a_(m_(i-1)+j)x_1~(d_m(i-1)+j,1)…x_(n_i)~d_(m_(i-1)+j,n_i)=b_r,r=1,…,k当指数满足一定条件时,在F~(n_s_k)上解数的一个直接公式,这里d_(ij)＞0,a_i∈F~*,b_i∈F,0= s_0＜s_1＜…＜s_k,0=m_0＜m_1＜…＜m_(s_k),0=n_0＜n_1＜…＜n_(s_k), m_1≤n_1,…,m_(s_k)≤n_(s_k)．
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| 关 键 词： | 有限域 方程的解数 矩阵 |
| 文章编号： | 0583-1431（2007）03-0653-08 |
| 收稿时间： | 2005-10-26 |
| 修稿时间： | 2005-10-26 |
An Explicit Formula for the Number of Solutions of Certain System of Equations over Finite Fields |
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| Ji Ming YANG.An Explicit Formula for the Number of Solutions of Certain System of Equations over Finite Fields[J].Acta Mathematica Sinica,2007,50(3):653-660. |
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| Authors: | Ji Ming YANG |
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| Institution: | Department of Mathematics, Yuxi Teachers College, Yuxi 653100, P. R. China |
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| Abstract: | Let F=F_q(q=p~f,f≥1,p is an odd prime number).In this paper,we get an explicit formula for the number of F-rational solutions of the following systems of equations defined over ∑_(i=s_(r-1)+1~(s_r)∑_(j=1)~(m_i-m_(i-1))a_(m_(i-1)+j)x_1~(d_m(i-1)+j,1)…x_(n_i)~d_(m_(i-1)+j,n_i)=b_r,r=1,…,k where dij＞0 satisfying certain conditions,a_i∈F~*,b_i∈F,0= s_0＜s_1＜…＜s_k,0=m_0＜m_1＜…＜m_s_k,0=n_0o＜n_1＜…＜n_s_k, m_1≤n_1,…,m_s_k≤n_s_k. |
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| Keywords: | finite field solution of equation matrix |
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