Enumerating $D_4$ Quartics and a Galois Group Bias Over Function Fields

Daniel Keliher

Enumerating $D_4$ Quartics and a Galois Group Bias Over Function Fields

Number Theory 2020-09-22 v1

Authors: Daniel Keliher

Abstract

We give an asymptotic formula for the number of $D_4$ quartic extensions of a function field with discriminant equal to some bound, essentially reproducing the analogous result over number fields due Cohen, Diaz y Diaz, and Olivier, but with a stronger error term. We also study the relative density of $D_4$ and $S_4$ quartic extensions of a function field and show that with mild conditions, the number of $D_4$ quartic extensions can far exceed the number of $S_4$ quartic extensions

Cite

@article{arxiv.2009.09274,
  title  = {Enumerating $D_4$ Quartics and a Galois Group Bias Over Function Fields},
  author = {Daniel Keliher},
  journal= {arXiv preprint arXiv:2009.09274},
  year   = {2020}
}

Comments

19 pages

Related papers

View all related →