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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The imaginary abelian number fields of $2$-power degrees with ideal class groups of exponent $\leq 2$
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by Jeoung-Hwan Ahn and Soun-Hi Kwon PDF
Math. Comp. 81 (2012), 533-554 Request permission

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 $\le 2$ 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
  • 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.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 533-554
  • MSC (2010): Primary 11R29, 11R20
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02509-3
  • MathSciNet review: 2833507