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Most totally real fields do not have universal forms or the Northcott property
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DOI：10.1073/pnas.2419414122.png)
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Abstract
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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.
Keywords:
universal quadratic form
totally real field
infinite extensions
Northcott property|
totally positive units
Journal
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IF:
9.1
Papers:
10.8W
Citations:
73.5W
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Cited Papers