A Barban-Davenport-Halberstam asymptotic for number fields
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Abstract:
Let $K$ be a fixed number field, and assume that $K$ is Galois over $\mathbb {Q}$. Previously, the author showed that when estimating the number of prime ideals with norm congruent to $a$ modulo $q$ via the Chebotarëv Density Theorem, the mean square error in the approximation is small when averaging over all $q\le Q$ and all appropriate $a$. In this article, we replace the upper bound by an asymptotic formula. The result is related to the classical Barban-Davenport-Halberstam Theorem in the case $K=\mathbb {Q}$.References
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Additional Information
- Ethan Smith
- Affiliation: Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931-1295
- Email: ethans@mtu.edu
- Received by editor(s): July 28, 2009
- Received by editor(s) in revised form: October 15, 2009, and October 30, 2009
- Published electronically: March 3, 2010
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2301-2309
- MSC (2010): Primary 11N36, 11R44
- DOI: https://doi.org/10.1090/S0002-9939-10-10303-7
- MathSciNet review: 2607859