Lifting problem for universal quadratic forms over totally real cubic number fields

Abstract

Lifting problem for universal quadratic forms asks for totally real number fields $K$ that admit a positive definite quadratic form with coefficients in $\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper, we show that $K=\mathbb{Q}({\zeta }_7+{\zeta }_7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.

12 pages

References in corpus (1)

• Universal quadratic forms and indecomposables in number fields: A survey

Cited by in corpus (2)

• Sails for universal quadratic forms
• Universal quadratic forms and Dedekind zeta functions