Counting nilpotent Galois extensions

Details Counting nilpotent Galois extensions Counting nilpotent Galois extensions

2001-12-04

arxiv.org/abs/math/0112318v1

Mathematics

Number Theory

Scientific paper

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.

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