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Number fields without universal quadratic forms of small rank exist in most degrees

Published online by Cambridge University Press:  06 May 2022

Charles University, Faculty of Mathematics and Physics, Department of Algebra, Sokolovská 49/83, 18675 Praha 8, Czech Republic. e-mails:,


We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.

Research Article
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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The author was supported by Czech Science Foundation GAČR, grant 21-00420M, and by Charles University, projects PRIMUS/20/SCI/002 and UNCE/SCI/022.


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