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On Ono’s problem for quadratic fields. (English) Zbl 0780.11050
Für einen quadratischen Zahlkörper \(k\) sei \(d_ k\) die Diskriminante, \(h_ k\) die Klassenzahl und \(M_ k\) die Minkowski- Schranke von \(k\) (\(M_ k=\sqrt{d_ k}/2\), falls \(k\) reell; \(M_ k=2\sqrt{-d_ k}/\pi\), falls \(k\) imaginär). Der Autor bestimmt (unter Voraussetzung von GRH) alle quadratischen Zahlkörper \(k\) mit folgender Eigenschaft: \(h_ k\) ist ungerade, und \((d_ k/p)\neq 1\) für alle Primzahlen \(p\leq M_ k\) (es gibt 42 solche Körper). Resultate von ähnlichem Typ wurden von S. Louboutin, R. A. Mollin und H. C. Williams erzielt [siehe Can. J. Math. 44, 824-842 (1992; Zbl 0771.11039)] und die dort zitierte Literatur.
MSC:
11R11 Quadratic extensions
11R29 Class numbers, class groups, discriminants
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