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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

A Bombieri-Vinogradov theorem for all number fields


Authors: M. Ram Murty and Kathleen L. Petersen
Journal: Trans. Amer. Math. Soc. 365 (2013), 4987-5032
MSC (2010): Primary 11M26; Secondary 11M06, 11N36
Published electronically: December 13, 2012
MathSciNet review: 3066777
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Abstract: The classical theorem of Bombieri and Vinogradov is generalized to a non-abelian, non-Galois setting. This leads to a prime number theorem of ``mixed-type'' for arithmetic progressions ``twisted'' by splitting conditions in number fields. One can view this as an extension of earlier work of M. R. Murty and V. K. Murty on a variant of the Bombieri-Vinogradov theorem. We develop this theory with a view to applications in the study of the Euclidean algorithm in number fields and arithmetic orbifolds.


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Additional Information

M. Ram Murty
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: murty@mast.queensu.ca

Kathleen L. Petersen
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: petersen@math.fsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05805-3
Received by editor(s): July 26, 2010
Received by editor(s) in revised form: December 17, 2011, and February 7, 2012
Published electronically: December 13, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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