CM-fields with relative class number one |
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| Authors: | Geon-No Lee Soun-Hi Kwon |
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| Institution: | Department of Mathematics Education, Korea University, 136-701, Seoul, Korea ; Department of Mathematics Education, Korea University, 136-701, Seoul, Korea |
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| Abstract: | We will show that the normal CM-fields with relative class number one are of degrees  . Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees  , and the CM-fields with class number one are of degrees  . By many authors all normal CM-fields of degrees  with class number one are known except for the possible fields of degree  or  . 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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| Keywords: | CM-fields class numbers relative class numbers Dedekind zeta functions |
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