Preprint
Asymptotics of number fields and the Cohen-Lenstra heuristics
Zusammenfassung
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.
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@article{urn:nbn:de:hebis:34-200604069117,
author={Klüners, Jürgen},
title={Asymptotics of number fields and the Cohen-Lenstra heuristics},
year={2005}
}
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2006-04-06T13:57:37Z 2006-04-06T13:57:37Z 2005 urn:nbn:de:hebis:34-200604069117 http://hdl.handle.net/123456789/200604069117 202851 bytes application/pdf eng Universität Kassel, FB 17, Mathematik/Informatik Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Gruppentheorie Asymptotics of number fields Cohen-Lenstra heuristics 510 Asymptotics of number fields and the Cohen-Lenstra heuristics Preprint 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. open access Klüners, Jürgen Mathematische Schriften Kassel 05, 12 Mathematische Schriften Kassel 05, 12
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