摘要
设整数m>1,m=是m的标准分解式,1≤k≤n,f_1,…,f_k是k个n元整系数多项式。本文证明了:1)f_1,…,f_k是模m的正交组当且仅当f_1,…,f_k是模的正交组,j=1,…,t.2)设f_1,…,f_k是模p的正交组,且对任一组整数a_1,…,a_k,均有秩(Jmodp)=k,则f_1,…,f_k是模p ̄l的正交组,l>1.这里p是一个素数,J是f_1…,f_k的Jacobi矩阵.
Let m>1,1≤k≤n,and In this paper,the authors proved following results : 1)The system off_1 ,…,f_k is orthogonal modulo m if and only ifthe system off_1,…,f_k is orthogonal modulo ,j=1,…,t where are distinctprimes,l_j≥1,j=1,…,t. 2) Let p be a prime and h > 1. If the system of f_1,…,f_k iS orthogonalmodulo p and for any(a_1,…,a_k)∈Z ̄(k) the rank of,J mod p=k, then the system of f_1,…,f_k isorthogonal modulo p ̄k, where J denotes the Jacobi matrix of f_1,…,f_k
出处
《四川大学学报(自然科学版)》
CAS
CSCD
1994年第4期439-441,共3页
Journal of Sichuan University(Natural Science Edition)
基金
高等学校博士学科点专项科研基金
关键词
多项式
正交组
模
整数
orthogonal systems of polynomials in several indeterminates , Jacobi matrix , Chineseremainde theorem