Most totally real fields do not have universal forms or the Northcott property.
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- Record sourced from PubMed, PMID 40377997.
- Also identified by DOI 10.1073/pnas.2419414122 and PMC identifier 12107117.
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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 theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.