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

Abstract

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.

6 pages

References in corpus (2)

• Universal quadratic forms, small norms and traces in families of number fields
• Can we recover an integral quadratic form by representing all its subforms?

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• Additive structure of non-monogenic simplest cubic fields
• There is no 290-Theorem for higher degree forms
• Failures of integral Springer's Theorem
• Generalizing Hurwitz's quaternionic proof of Lagrange's and Jacobi's four-square theorems