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

 

CM-fields with relative class number one


Authors: Geon-No Lee and Soun-Hi Kwon
Journal: Math. Comp. 75 (2006), 997-1013
MSC (2000): Primary 11R29, 11R42
Published electronically: November 29, 2005
MathSciNet review: 2197004
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Abstract | References | Similar Articles | Additional Information

Abstract: We will show that the normal CM-fields with relative class number one are of degrees $ \leq 216$. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees $ \leq 96$, and the CM-fields with class number one are of degrees $ \leq 104$. By many authors all normal CM-fields of degrees $ \leq 96$ with class number one are known except for the possible fields of degree $ 64$ or $ 96$. Consequently the class number one problem for normal CM-fields is solved under the Generalized Riemann Hypothesis except for these two cases.


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Additional Information

Geon-No Lee
Affiliation: Department of Mathematics Education, Korea University, 136-701, Seoul, Korea
Email: thisknow@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/S0025-5718-05-01811-9
PII: S 0025-5718(05)01811-9
Keywords: CM-fields, class numbers, relative class numbers, Dedekind zeta functions
Received by editor(s): January 19, 2005
Received by editor(s) in revised form: February 27, 2005
Published electronically: November 29, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.