The imaginary abelian number fields with class numbers equal to their genus class numbers
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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It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of 2-power degrees with class numbers equal to their genus class numbers.
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Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.
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Let K be an imaginary quadratic field with class number one and let p ⊂ OK be a degree one prime ideal of norm p not dividing 6dK . In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields Kp heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura’s reciprocity law. We have...
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The classical class number problem of Gauss asks for a classification of all imaginary quadratic fields with a given class number N . The first complete results were for N = 1 by Heegner, Baker, and Stark. After the work of Goldfeld and Gross-Zagier, the task was a finite decision problem for any N . Indeed, after Oesterlé handled N = 3, in 1985 Serre wrote, “No doubt the same method will work ...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2000
ISSN: 1246-7405
DOI: 10.5802/jtnb.283