Counting nilpotent Galois extensions
By J. Klueners, Gunter Malle. 2001
79 citations recorded by the source corpus.
We obtain strong information on the asymptotic behaviour of the counting function for nilpotent Galois extensions with bounded discriminant of arbitrary number fields. This extends previous investigations for the case of abelian groups. In particular, the result confirms a conjecture by the second author on this function for arbitrary groups in the nilpotent case. We further prove compatibility of the conjecture with taking wreath products with the cyclic group of order 2 and give examples in degree up to 8.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7fccf173420e47292a7bd8f14022167a94ef0c36
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- A counter example to Malle's conjecture on the asymptotics of discriminants (2004, background): “a(G) log(x)b(k,G)−1, 1 2 JURGEN KL¨ UNERS¨ where a(G) and b(k,G) are given as above. This conjecture is proved for abelian groups [9]. For all number fields k and all nilpotent groups G it is shown in [6] that limsup x→∞ logZ(k,G;x) logx ≤ a(G). If we furthermore assume that G is in its regular repre”