A Barban-Davenport-Halberstam asymptotic for number fields

Author:
Ethan Smith

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

Published electronically:
March 3, 2010

MathSciNet review:
2607859

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a fixed number field, and assume that is Galois over . Previously, the author showed that when estimating the number of prime ideals with norm congruent to modulo via the Chebotarëv Density Theorem, the mean square error in the approximation is small when averaging over all and all appropriate . 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 .

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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

DOI:
https://doi.org/10.1090/S0002-9939-10-10303-7

Keywords:
Generalized Siegel-Walfisz theorem,
Barban-Davenport-Halberstam Theorem

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

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.