The asymptotics of nilpotent Galois groups

TL;DR

This paper establishes an upper bound on how the number of number fields with nilpotent Galois groups grows asymptotically, advancing understanding of their distribution.

Contribution

It provides the first known upper bound for the asymptotic count of number fields with nilpotent Galois groups, a significant step in inverse Galois theory.

Findings

Derived an explicit upper bound for counting functions

Enhanced understanding of distribution of nilpotent Galois groups

Paved the way for future asymptotic analyses

Abstract

We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups.