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arXiv · 1210.3863

A Barban-Davenport-Halberstam asymptotic for number fields

Ethan Smith
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Abstract

Let $K$ be a fixed number field, and assume that $K$ is Galois over $\qq$. 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 $q\le Q$ 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 $K=\qq$.

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Ethan Smith. 2012-10-15. A Barban-Davenport-Halberstam asymptotic for number fields. https://doi.org/10.1090/s0002-9939-10-10303-7

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