Most totally real fields do not have universal forms or Northcott property
Number Theory
2025-05-29 v2
Abstract
We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.
Cite
@article{arxiv.2409.11082,
title = {Most totally real fields do not have universal forms or Northcott property},
author = {Nicolas Daans and Vitezslav Kala and Siu Hang Man and Martin Widmer and Pavlo Yatsyna},
journal= {arXiv preprint arXiv:2409.11082},
year = {2025}
}
Comments
author accepted manuscript, 13 pages