Ambiguous classes in quadratic fields. (English) Zbl 0790.11076

Sei \(K\) ein reell-quadratischer Zahlkörper mit Diskriminante \(\Delta\), seien \(q_ 1,\dots,q_ n\) paarweise teilerfremde quadratfreie Teiler von \(\Delta\) und \(Q_ 1,\dots,Q_ n\) deren Primteiler in \(K\). Sei \[ F_ i(x)= q_ i x^ 2+ (\alpha_ i- 1)q_ i x+(4q_ i)^{- 1}(\alpha_ i q^ 2_ i- q^ 2_ i-\Delta) \] mit \(\alpha_ i=1\), falls \(4q_ i|\Delta\) und \(\alpha_ i=2\) sonst. Der Autor beweist ein Kriterium folgenden Typs: Stellen die quadratischen Polynome \(F_ i(z)\) hinreichend viele Primzahlen dar, so besteht die Klassengruppe von \(K\) nur aus den Klassen von \(1,Q_ 1,\dots,Q_ n\).


11R11 Quadratic extensions
11R29 Class numbers, class groups, discriminants
11Y40 Algebraic number theory computations
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