Asymptotics of number fields and the Cohen--Lenstra heuristics
Jürgen Klüners
Abstract
We study the asymptotics conjecture of Malle for dihedral groups D of order 2, where is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.
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