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Asymptotics of number fields and the Cohen-Lenstra heuristics

Klüners, Jürgen

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l 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.

Citation
In: Mathematische Schriften Kassel 05, 12 / (2005) , S. ; 
@article{urn:nbn:de:hebis:34-200604069117,
  author    ={Klüners, Jürgen},
  title    ={Asymptotics of number fields and the Cohen-Lenstra heuristics},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2005}
}