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Arithmetic properties of class numbers of imaginary quadratic fields. (English) Zbl 1148.11056

Summary: Under the assumption of the well-known heuristics of Cohen and Lenstra (and the new extensions we propose) we give proofs of several new properties of class numbers of imaginary quadratic number fields, including theorems on smoothness and normality of their divisors. Some applications in cryptography are also discussed.

MSC:

11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
11R47 Other analytic theory
94A60 Cryptography
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