English

The local zeta function in enumerating quartic fields

Number Theory 2021-05-25 v3

Abstract

An exact formula is obtained for the Fourier transform of the local condition of maximality modulo primes p>3p>3 in the prehomogeneous vector space 2Sym2(Zp3)2 \otimes \mathrm{Sym}^2(\mathbb{Z}_p^3) parametrizing quartic fields, thus solving the local `quartic case' in enumerating quartic fields.

Cite

@article{arxiv.1806.01372,
  title  = {The local zeta function in enumerating quartic fields},
  author = {Robert Hough},
  journal= {arXiv preprint arXiv:1806.01372},
  year   = {2021}
}

Comments

Minor corrections

R2 v1 2026-06-23T02:18:51.773Z