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

Ethan Smith

doi:10.1016/j.jnt.2009.05.005

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

Number Theory 2012-10-16 v1

Authors: 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 Chebotar\"ev 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.

Keywords

number fields Barban-Davenport-Halberstam theorem Chebotar"ev density theorem mean square error large sieve inequality prime ideals

Cite

@article{arxiv.1210.3862,
  title  = {A generalization of the Barban-Davenport-Halberstam Theorem to number fields},
  author = {Ethan Smith},
  journal= {arXiv preprint arXiv:1210.3862},
  year   = {2012}
}

Comments

Preprint of an old paper

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