On the ideal class groups of the $p$-class fields of quadratic number fields
نویسندگان
چکیده
منابع مشابه
Exponents of the ideal class groups of CM number fields
Since class numbers of CM number fields of a given degree go to infinity with the absolute values of their discriminants, it is reasonable to ask whether the same conclusion still holds true for the exponents of their ideal class groups. We prove that under the assumption of the Generalized Riemann Hypothesis this is indeed the case. 1991 Mathematics Subject Classification. Primary 11R29, 11R21.
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The author has computed the class groups of all complex quadratic number fields Q(\f^~D) °f discriminant D for 0 < D < 4000000. In so doing, it was found that the first occurrences of rank three in the 3-Sylow subgroup are D = 3321607 = prime, class group C(3) x C(3) x C(9.7) (C(n) a cyclic group of order n), and D = 3640387 = 421.8647, class group C(3) X C(3) X C(9.2). The author has also foun...
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15 صفحه اولImprovements in the computation of ideal class groups of imaginary quadratic number fields
We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.
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Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these results to CM-fields by using class field theory. Although we will only need some special cases, we have also decided to include a few results on Hasse’s unit...
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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.68.62