A variant of the Barban-Davenport-Halberstam Theorem

Abstract

Let $L/K$ be a Galois extension of number fields. The problem of counting the number of prime ideals $\mathfrak{p}$ of $K$ with fixed Frobenius class in $\mathrm{Gal}(L/K)$ and norm satisfying a congruence condition is considered. We show that the square of the error term arising from the Chebotarëv Density Theorem for this problem is small "on average." The result may be viewed as a variation on the classical Barban-Davenport-Halberstam Theorem.

References in corpus (2)

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

Cited by in corpus (1)

• Average Frobenius distribution for the degree two primes of a number field