函数域Fq(T,lDl+d)的基本单位

设Fq(T)=k, p是Fq的特征, l是奇素数, (Z/lZ)*= q ,M=Dl+d,d=ld0, Fq*, d0,D是Fq［T］中首一多项式, D 1,d0|Dl-1, M是l-幂自由的,记=(lM-D)l d,K为K=k(lM)的基本单位, K<0, 我们有结果: =Kpilj, j 0,1, 0 i e, 其中e是l的p-adic表示中p的最高幂次数.

Fundamental Unit of Fq(T,lDl+d)

Let k=Fq(T), p the characteristic of Fq,l an odd prime number such that q is a generator of (Z/l Z)*, M=Dl+d where d=ld0, Fq*, d0 and D are monic polynomials in Fq［T］, D 1, d0|Dl-1, M is l th power-free. Let =(lM-D)l d, K is the fundamental unit of k(lM), K<0. We proved that=Kpilj where j 0,1, 0 i e,e is the highest power-degree of p in the p-adic expansion of l.