Asymptotics of number fields and the Cohen–Lenstra heuristics

Jürgen Klüners
2006 Journal de Théorie des Nombres de Bordeaux  
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.
doi:10.5802/jtnb.561 fatcat:fl54ptjwcbcxjdmq4atps3pjq4