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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The imaginary abelian number fields of $ 2$-power degrees with ideal class groups of exponent $ \leq 2$


Authors: Jeoung-Hwan Ahn and Soun-Hi Kwon
Journal: Math. Comp. 81 (2012), 533-554
MSC (2010): Primary 11R29, 11R20
Published electronically: July 1, 2011
MathSciNet review: 2833507
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Abstract: In this paper, assuming the Generalized Riemann Hypothesis, we determine all imaginary abelian number fields $ N$ of 2-power degrees with ideal class groups of exponents $ \le2$ for which the 2-ranks of the Galois group of $ N$ over $ \mathbb{Q}$ are equal to 2.


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Additional Information

Jeoung-Hwan Ahn
Affiliation: Department of Mathematics Education, Korea University, 136-701, Seoul, Korea
Email: jh-ahn@korea.ac.kr

Soun-Hi Kwon
Affiliation: Department of Mathematics Education, Korea University, 136-701, Seoul, Korea
Email: sounhikwon@korea.ac.kr

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02509-3
PII: S 0025-5718(2011)02509-3
Keywords: Class group, class numbers, relative class numbers
Received by editor(s): November 15, 2009
Received by editor(s) in revised form: November 29, 2010
Published electronically: July 1, 2011
Additional Notes: This research was supported by Grant KRF-2008-313-C00008.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.