Cohen-Lenstra heuristics and local conditions

Cohen-Lenstra Heuristics of Quadratic Number Fields

We establish a link between some heuristic asymptotic formulas (due to Cohen and Lenstra) concerning the moments of the p–part of the class groups of quadratic fields and formulas giving the frequency of the values of the p–rank of these class groups. Furthermore we report on new results for 4–ranks of class groups of quadratic number fields.

New Computations Concerning the Cohen-Lenstra Heuristics

Invariants for A4 Fields and the Cohen-lenstra Heuristics

In 1983, Cohen and Lenstra in [1] provided a heuristic for estimating the distribution of class groups of quadratic fields, and, more generally, abelian extensions of Q. These heuristics were extended by Cohen and Martinet in [2] and [3] in 1987 and 1990 to fields of more general type. Recently, Malle in [9] has subjected these heuristics to careful scrutiny by computing class groups for many f...

Asymptotics of Number Fields and the Cohen–lenstra Heuristics

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 a...

Asymptotics of number fields and the Cohen – Lenstra heuristics par

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 a...