Density of $p$-adic polynomials generating extensions with fixed splitting type
Number Theory
2022-11-24 v2
Abstract
We prove that the density of polynomials over a local field generating an \'etale extension with specified splitting type is a rational function in terms of the size of the residue field of in the case where the splitting type is tame. Moreover, we give a computable recursive formula for these densities and compute the asymptotics of this density as the size of the residue field tends to infinity.
Cite
@article{arxiv.2211.10425,
title = {Density of $p$-adic polynomials generating extensions with fixed splitting type},
author = {John Yin},
journal= {arXiv preprint arXiv:2211.10425},
year = {2022}
}