有限域上一类方程组的解数公式

设F_q为一个q元有限域,其中q=p~s(s≥1),p是一个奇素数.本文给出下列方程组在F_q上的解数公式:a_(k1)x_1~(d_(11)~((k)))...x_(n_1)~(d_(1n_1)~((k)))+...+a_(k,s_1)x_1~(d_(s_1,1)~((k)))...x_(n_1)~(d_(s_1,n_1)~((k)))+a_(k,s_1)+1x_1~(d_(s_1+1,1)~((k)))...x_(n_2)~(d_(s_1+1,n_2)~((k)))+...a_(k,s_2)x_1~(d_(s_2,1)~((k)))...x_(n_2)~(d_(s_2,1)~((k)))...x_(n_2)~(d_(s_2,n_2)~((k)))=b_k,k=1,...,m,其中0s_1s_2,0n_1n_2,a_(ki)∈F_q~*,b_k∈F_q,d_(ij)~(k)0(k=l,...,m,i=1,...,s_2,j=1,...,n_2).特别当ms_1≤n_1,ms_2≤n_2,d_(ij)~(k)满足一定条件时,得到了明确的解数公式.