Inductive Method for Counting Number Fields

We propose a general framework to inductively prove new results for counting number fields. By using this method, we prove the precise asymptotic distribution of G -extensions for a family of Galois groups G  that could be constructed via taking towers of extensions. The key ingredient is a uniform estimate on the number of relative extensions with dependency on the base field. This is a joint work with Robert J.Lemke Oliver and Melanie Matchett Wood.