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A Barban-Davenport-Halberstam asymptotic for number fields
Author(s):
Ethan
Smith
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2301-2309.
MSC (2010):
Primary 11N36, 11R44
Posted:
March 3, 2010
MathSciNet review:
2607859
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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:
10.1090/S0002-9939-10-10303-7
PII:
S 0002-9939(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
Posted:
March 3, 2010
Communicated by:
Ken Ono
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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