Distribution of genus numbers of abelian number fields
arXiv:2209.10659 · doi:10.1112/jlms.12737
Abstract
We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the genus number and show that any given genus number appears only 0% of the time.
19 pages. Final version, accepted for publication in Journal of the London Mathematical Society. Published online at https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12737