Most totally real fields do not have universal forms or the Northcott property
成果类型：
Article
署名作者：
Daans, Nicolas; Kala, Vitezslav; Man, Siu Hang; Widmer, Martin; Yatsyna, Pavlo
署名单位：
Charles University Prague; KU Leuven; Graz University of Technology
刊物名称：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
ISSN/ISSBN：
0027-15270
DOI：
10.1073/pnas.2419414122
发表日期：
2025-05-20
关键词：
摘要：
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.