منابع مشابه
Class Groups of Quadratic Fields
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...
متن کاملQuadratic Fields with Special Class Groups
For every prime number p > 5 it is shown that, under certain hypotheses on x e Q , the imaginary quadratic fields Q( \/x2p 6xf + 1 ) have ideal class groups with noncyclic p-parts. Several numerical examples with p = 5 and 7 are presented. These include the field Q(v/-4805446123032518648268510536). The 7-part of its class group is isomorphic to C(7) x C(7) x C(7), where C(n) denotes a cyclic gr...
متن کاملQuadratic Fields with Cyclic 2-class Groups
For any integer k ≥ 1, we show that there are infinitely many complex quadratic fields whose 2-class groups are cyclic of order 2. The proof combines the circle method with an algebraic criterion for a complex quadratic ideal class to be a square. In memory of David Hayes.
متن کاملNumerical Results on Class Groups of Imaginary Quadratic Fields
– Originally, we only listed first occurrences of p-Sylow subgroups for primes p ≤ 173. In this paper, we present the entire list, for primes p ≤ 389. See Table 7. – When listing the first ∆ needing prime ideals of norm up to p, we pointed out an anomaly in the data at p = 181. Subsequent analysis has shown this to be a bug in our statistics gathering program. The data no longer contains any an...
متن کاملExperimental Results on Class Groups of Real Quadratic Fields
In an effort to expand the body of numerical data for real quadratic fields, we have computed the class groups and regulators of all real quadratic fields with discriminant ∆ < 10. We implemented a variation of the group structure algorithm for general finite Abelian groups described in [2] in the C++ programming language using built-in types together with a few routines from the LiDIA system [...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1987
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1987-0866100-9