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 ⩽ Q and all appropriate a. Using a large sieve inequality, we obtain an upper bound similar to the Barban–Davenport–Halberstam Theorem.