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.

Accepted version, 28 pages

References in corpus (1)

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

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