论文标题
Chebotarev密度定理的补充
A supplement to Chebotarev's density theorem
论文作者
论文摘要
让$ l/k $是Galois Group $ g $的数字字段的Galois扩展。我们表明，如果$ k $在$ l $中完全分配的$ k $中的主要理想密度倾向于$ 1/| g | $带有节省误差术语，那么$ k $中的质量理想的密度是$ k $的frobenius是给定的frobacy类$ c \ subset g $，倾向于$ | c |/| g | c |/| g | $具有相同的节省错误项。我们通过将相应的Dirichlet系列的极点与$ζ_L（s）/ζ_K（S）$相关的零来推断出来。
Let $L/K$ be a Galois extension of number fields with Galois group $G$. We show that if the density of prime ideals in $K$ that split totally in $L$ tends to $1/|G|$ with a power saving error term, then the density of prime ideals in $K$ whose Frobenius is a given conjugacy class $C\subset G$ tends to $|C|/|G|$ with the same power saving error term. We deduce this by relating the poles of the corresponding Dirichlet series to the zeros of $ζ_L(s)/ζ_K(s)$.
