Asymptotics of number fields and the Cohen–Lenstra heuristics

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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Klüners, Jürgen. "Asymptotics of number fields and the Cohen–Lenstra heuristics." Journal de Théorie des Nombres de Bordeaux 18.3 (2006): 607-615. <http://eudml.org/doc/249652>.

@article{Klüners2006,
abstract = {We study the asymptotics conjecture of Malle for dihedral groups $D_\ell $ of order $2\ell $, where $\ell $ 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.},
affiliation = {Heinrich-Heine-Universität Düsseldorf, Mathematisches Institut Universitätsstr. 1, 40225 Düsseldorf, Germany},
author = {Klüners, Jürgen},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Cohen-Lenstra heuristics; Galois groups},
language = {eng},
number = {3},
pages = {607-615},
publisher = {Université Bordeaux 1},
title = {Asymptotics of number fields and the Cohen–Lenstra heuristics},
url = {http://eudml.org/doc/249652},
volume = {18},
year = {2006},
}

TY - JOUR
AU - Klüners, Jürgen
TI - Asymptotics of number fields and the Cohen–Lenstra heuristics
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 3
SP - 607
EP - 615
AB - We study the asymptotics conjecture of Malle for dihedral groups $D_\ell $ of order $2\ell $, where $\ell $ 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.
LA - eng
KW - Cohen-Lenstra heuristics; Galois groups
UR - http://eudml.org/doc/249652
ER -

References

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