CM-fields with relative class number one

Lee, Geon-No; Kwon, Soun-Hi

doi:10.1090/S0025-5718-05-01811-9

CM-fields with relative class number one
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by Geon-No Lee and Soun-Hi Kwon;

Math. Comp. 75 (2006), 997-1013

DOI: https://doi.org/10.1090/S0025-5718-05-01811-9

Published electronically: November 29, 2005

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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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