Imaginary abelian number fields with class number one
نویسندگان
چکیده
منابع مشابه
Class Numbers of Imaginary Abelian Number Fields
Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...
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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 • 163 , which is the conductor of the biquadratic number field Q(\/-67, v'—163).
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Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.
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We will show that the normal CM-fields with relative class number one are of degrees ≤ 216. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees ≤ 96, and the CM-fields with class number one are of degrees ≤ 104. By many authors all normal CM-fields of degrees ≤ 96 with class number one are known except for the possib...
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In this paper we compute the relative class number of all imaginary Abelian fields of prime conductor below 10000. Our approach is based on a novel multiple evaluation technique, and, assuming the ERH, it has a running time of O(p2 log(p) log log(p)), where p is the conductor of the field.
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1972
ISSN: 0040-8735
DOI: 10.2748/tmj/1178241490