关于一类数域的子域(英文)

ON THE SUBFIELDS OF A CLASS OF NUMBER FIELDS

设p是一个奇系数,m,r为两个正整数满足m不含pr次因子且p｜m.作者得到了有理数域Q上的不可约多项式xpr-m的分裂域K=Q(prm,ζ)的pk(1≤k≤2r-1)次子域的个数的一个下界.

Let p be an odd prime and m, r be positive integers satisfying that m is prth powerfree and p|m. The author obtained a lower bound of the number of the subfields of degree pk, where 1≤k≤2r-1, of the splitting field K of the irreducible binomial xpr-m.