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The 4-class ranks of quadratic extensions of certain real quadratic fields. (English) Zbl 0694.12003
Author’s summary: “Let F be a real quadratic extension of $${\mathbb{Q}}$$ in which exactly one prime ramifies. Let K be a quadratic extension of F, and let $$R_ K$$ denote the 4-class rank of K. We specify how likely it is that $$R_ K=0,1,2,...$$. The formulas we obtain are analogous to formulas conjectured by Cohen and Martinet in the prime-to-2 part of the ideal class group of K.”
Reviewer: J.Hinz

##### MSC:
 11R11 Quadratic extensions 11R37 Class field theory 11R23 Iwasawa theory
##### Keywords:
quadratic extension; 4-class rank; ideal class group
Full Text:
##### References:
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