English

Lower bounds for counting $A_4$-quartic fields

Number Theory 2025-10-08 v1

Abstract

A conjecture of Malle predicts the quantity of number fields with bounded discriminant of given Galois group. We present a lower bound matching this in the case of quartic fields with Galois group A4A_4.

Cite

@article{arxiv.2510.05248,
  title  = {Lower bounds for counting $A_4$-quartic fields},
  author = {Daniel Loughran and Ross Paterson},
  journal= {arXiv preprint arXiv:2510.05248},
  year   = {2025}
}

Comments

24 pages, comments welcome!

R2 v1 2026-07-01T06:19:55.982Z