Corrigenda for the determination of the imaginary abelian number fields with class number one
نویسندگان
چکیده
منابع مشابه
The Determination of the Imaginary Abelian Number Fields with Class Number One
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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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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Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.
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متن کاملThe Dirichlet Class Number Formula for Imaginary Quadratic Fields
Z[ √ −5] = {a+ b √ −5 : a, b ∈ Z}, because 2, 3, and 1± √ −5 are irreducible and nonassociate. These notes present a formula that in some sense measures the extent to which unique factorization fails in environments such as Z[ √ −5]. Algebra lets us define a group that measures the failure, geometry shows that the group is finite, and analysis yields the formula for its order. To move forward t...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1992
ISSN: 0386-2194
DOI: 10.3792/pjaa.68.74