Distribution of genus numbers of abelian number fields
Number Theory
2023-04-25 v2
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.
Keywords
Cite
@article{arxiv.2209.10659,
title = {Distribution of genus numbers of abelian number fields},
author = {Christopher Frei and Daniel Loughran and Rachel Newton},
journal= {arXiv preprint arXiv:2209.10659},
year = {2023}
}
Comments
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