Barban-Davenport-Halberten定理的一个变体
A variant of the Barban-Davenport-Halberstam Theorem
摘要：
设$L/K$是数域的Galois扩张.考虑了在$\mathrm{Gal}(L/K)$中Frobenius类固定且范数满足同余条件的$K$的素理想$\mathfrak p$的个数的计算问题.我们表明，这个问题的Chebotarëv密度定理所产生的误差项的平方是小的“平均。这个结果可以被看作是经典的Barban-Davenport-Halberten定理的一个变体。
英文摘要：
Let $L/K$ be a Galois extension of number fields. The problem of counting the number of prime ideals $\mathfrak p$ of $K$ with fixed Frobenius class in $\mathrm{Gal}(L/K)$ and norm satisfying a congruence condition is considered. We show that the square of the error term arising from the Chebotarëv Density Theorem for this problem is small "on average." The result may be viewed as a variation on the classical Barban-Davenport-Halberstam Theorem.
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