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

Abstract

For a fixed number field $K$, we consider the mean square error in estimating the number of primes with norm congruent to $a$ modulo $q$ by the Chebotarëv Density Theorem when averaging over all $q\le Q$ and all appropriate $a$. Using a large sieve inequality, we obtain an upper bound similar to the Barban-Davenport-Halberstam Theorem.

Preprint of an old paper

Cited by in corpus (2)

• Average Frobenius distribution for elliptic curves defined over finite Galois extensions of the rationals
• A Barban-Davenport-Halberstam asymptotic for number fields