ARITHMETIC PROPERTIES OF CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS

Safuat Hamdy (United Arab Emirates) and Filip Saidak (U. S. A.)

Abstract

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.

Keywords and phrases: divisors of class numbers, Cohen-Lenstra heuristics, Erdös-Kac theorem.