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arXiv · 1210.3862

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

Ethan Smith
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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.

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Ethan Smith. 2012-10-15. A generalization of the Barban-Davenport-Halberstam Theorem to number fields. https://doi.org/10.1016/j.jnt.2009.05.005

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