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The determination of the imaginary abelian number fields with class number one


Author: Ken Yamamura
Journal: Math. Comp. 62 (1994), 899-921
MSC: Primary 11R20; Secondary 11R29
DOI: https://doi.org/10.1090/S0025-5718-1994-1218347-3
MathSciNet review: 1218347
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Abstract: In this paper, we determine all the imaginary abelian number fields with class number one. There exist exactly 172 imaginary abelian number fields with class number one. The maximal conductor of these fields is $ 10921 = 67 \cdot 163$, which is the conductor of the biquadratic number field $ {\mathbf{Q}}(\sqrt { - 67} ,\sqrt { - 163} )$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1994-1218347-3
Keywords: Imaginary abelian number fields, class number, characters
Article copyright: © Copyright 1994 American Mathematical Society

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