The asymptotics of nilpotent Galois groups
J\"urgen Kl\"uners

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.
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Taxonomy
TopicsAnalytic Number Theory Research · Cryptography and Residue Arithmetic
