A Barban-Davenport-Halberstam asymptotic for number fields

الأصل · EN

Let K be a fixed number field, and assume that K is Galois over. Previously, the author showed that when estimating the number of prime ideals with norm congruent to a modulo q via the Chebotarëv Density Theorem, the mean square error in the approximation is small when averaging over all q≤ Q and all appropriate a. In this article, we replace the upper bound by an asymptotic formula. The result is related to the classical Barban-Davenport-Halberstam Theorem in the case K=.