Class number one problem for normal CM-fields |
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Authors: | Sun-Mi Park |
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Institution: | Department of Mathematics Education, Korea University, 136-701 Seoul, Republic of Korea |
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Abstract: | It is known that if we assume the Generalized Riemann Hypothesis, then any normal CM-field with relative class number one is of degree less than or equal to 96. All normal CM-fields of degree less than 48 with class number one are known. In addition, for normal CM-fields of degree 48 the class number one problem is partially solved. In this paper we will show that under the Generalized Riemann Hypothesis there is no more normal CM-fields with class number one except for the possible fields of degrees 64 or 96. |
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Keywords: | primary 11R29 secondary 11R21 |
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