| 特征≠2的有限域上对称矩阵方程解的计数公式及其q超几何级数表达 |
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| 引用本文： | 魏鸿增,张谊宾.特征≠2的有限域上对称矩阵方程解的计数公式及其q超几何级数表达[J].数学学报,1997,40(5):783-792. |
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| 作者姓名： | 魏鸿增 张谊宾 |
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| 作者单位： | 河北师范大学 |
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| 基金项目： | 国家自然科学基金,河北省教委科研项目 |
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| 摘 要： | 设Ｆｑ是特征≠２的有限域．本文利用Ｆｑ上奇异正交几何的理论，给出当Ａ，Ｂ分别是Ｆｑ上阶ｎ秩２ν＋δ和阶ｍ秩２ｓ＋γ的对称矩阵时，Ｆｑ上适合方程ＸＡＸ′＝Ｂ的秩ｋ的解Ｘ的个数和解Ｘ的个数的明显公式，并且用ｑ超几何级数简化表达解数公式．
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| 关 键 词： | 对称矩阵方程，奇异正交空间，q超几何级数 |
| 收稿时间： | 1995-9-25 |
| 修稿时间： | 1996-12-2 |
The Number of Solutions to the Symmetric Matrix Equation over a Finite Field of Ch.≠2 and Representation of Itsq hypergeometric Series |
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| Wei Hongzeng,Zhang Yibin.The Number of Solutions to the Symmetric Matrix Equation over a Finite Field of Ch.≠2 and Representation of Itsq hypergeometric Series[J].Acta Mathematica Sinica,1997,40(5):783-792. |
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| Authors: | Wei Hongzeng Zhang Yibin |
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| Institution: | Wei Hongzeng Zhang Yibin (Hebei Normal University, Shijiazhuang 050091, China) |
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| Abstract: | Let F q be a finite field with q elements,where q is a power of an odd prime. In this paper, using singular orthogonal goemetry over F q, we have given the number of solutions X of rank k and solutions X to the equation XAX′=B over F q, when A and B are symmetric matrices of order n, rank 2ν+δ and order m, rank 2s+γ, respectively. Finally, we have obtained simple representation of enumerational formulas using q hypergeometric series. |
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| Keywords: | Symmetric matrix equation Singular orthogonal space q hypergeometric series |
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