Universal quadratic forms and indecomposables over biquadratic fields

Martin Čech, Dominik Lachman, Josef Svoboda, Magdaléna Tinková and Kristýna Zemková

Mathematische Nachrichten, 2019, vol. 292, issue 3, 540-555

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. These are used to prove, over two particular biquadratic number fields Q(2,3) and Q(6,19), a lower bound on the number of variables of a universal quadratic forms.

Date: 2019
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https://doi.org/10.1002/mana.201800109

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:292:y:2019:i:3:p:540-555

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