THERE IS NO TENTH COMPLEX QUADRATIC FIELD WITH CLASS-NUMBER ONE
نویسندگان
چکیده
منابع مشابه
Computation of Real Quadratic Fields with Class Number One
A rapid method for determining whether the real quadratic field Sí = S(\/D) has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of .W and then uses the Generalized Riemann Hypothesis to rapidly estimate L(l, x) to the accuracy needed for determining whether or not the class number of 3£ is one. The results of running this algor...
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We enumerate all one class genera of definite ternary quadratic forms over number fields. For this, we construct all Gorenstein orders of type number one in definite quaternion algebras over number fields. Finally, we list all definite quaternion orders of ideal class number one.
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For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.
متن کاملReal Quadratic Orders with Large Class Number
Acknowledgements I am undoubtedly indebted to my two supervisors, Alf van der Poorten and Hugh Williams. Most students would feel lucky to have one good supervisor whereas I had the privilege of having two excellent mathematicians to guide me. Their help, wisdom and infinite patience has been invaluable, and I am very grateful for it. The Mathematics Department at Macquarie University has provi...
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We enumerate all positive definite ternary quadratic forms over number fields with class number at most 2. This is done by constructing all definite quaternion orders of type number at most 2 over number fields. Finally, we list all definite quaternion orders of ideal class number 1 or 2.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1967
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.57.2.216