Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields

Abstract

We establish an upper bound on the number of real multiquadratic fields that admit a universal quadratic lattice of a given rank, or contain a given amount of indecomposable elements modulo totally positive units, obtaining density zero statements. We also study the structure of indecomposable elements in real biquadratic fields, and compute a system of indecomposable elements modulo totally positive units for some families of real biquadratic fields.

arXiv commentAccepted version, 28 pages

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Cited by in corpus (5)

• Universal quadratic forms and Northcott property of infinite number fields
• Most totally real fields do not have universal forms or Northcott property
• Sails for universal quadratic forms
• Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables
• Additive structure of non-monogenic simplest cubic fields