A Barban-Davenport-Halberstam asymptotic for number fields

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 $K=\qq$.

Preprint of an old paper

References in corpus (1)

• A generalization of the Barban-Davenport-Halberstam Theorem to number fields

Cited by in corpus (1)

• Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals