A barban-davenport-halberstam asymptotic for number fields

Document Type

Article

Publication Date

7-1-2010

Abstract

Let K be a fixed number field, and assume that K is Galois over ℚ. 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- DavenportHalberstam Theorem in the case K = ℚ. © 2010 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society

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