2000
DOI: 10.1006/jnth.1999.2455
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Parametrization of the Quadratic Fields Whose Class Numbers are Divisible by Three

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Cited by 39 publications
(27 citation statements)
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“…Therefore, the splitting field of f α over ‫ޑ‬ is an unramified cyclic cubic extension of k, and hence the class number of k is divisible by 3. We easily see that the condition (i) in [6,Theorem] holds. Furthermore,…”
Section: Proofs Of Theoremsmentioning
confidence: 92%
“…Therefore, the splitting field of f α over ‫ޑ‬ is an unramified cyclic cubic extension of k, and hence the class number of k is divisible by 3. We easily see that the condition (i) in [6,Theorem] holds. Furthermore,…”
Section: Proofs Of Theoremsmentioning
confidence: 92%
“…D'après [4], le corps de décomposition de P définit une extension cubique cyclique non ramifiée de k, qu'on notera K diéderale sur Q (car disc(P ) = u 2 d) n'est pas un carré, et on a h K = ah 2 L , où h désigne le 3-nombre de classes de F (voir [6]). En se basant sur tout cela et à l'aide du logiciel PARI nous donnons des exemples qui illustrent les deux types de structure qu'on notera par alpha et delta.…”
Section: Unités Des Extensions Cubiques De Certains Sous-corpsunclassified
“…In [8], Kishi and Miyake give a characterization of all quadratic number fields with class number divisible by 3. The following is a function field analogue of Kishi and Miyake's result.…”
Section: -Rankmentioning
confidence: 99%