Most totally real fields do not have universal forms or Northcott property
arXiv:2409.11082 · doi:10.1073/pnas.2419414122
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.
author accepted manuscript, 13 pages