Universal quadratic forms and indecomposables over biquadratic fields

Abstract

The aim of this article is to study (additively) indecomposable algebraic integers OK of biquadratic number fields K and universal totally positive quadratic forms with coefficients in OK. There are given sufficient conditions for an indecomposable element of a quadratic subfield to remain indecomposable in the biquadratic number field K.

Furthermore, estimates are proven which enable algorithmization of the method of escalation over K.

Keywords

• indecomposable integer
• universal quadratic form
• biquadratic number field