Universal quadratic forms and indecomposables over biquadratic fields

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 indecompo...

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Bibliographic Details
Published in:Mathematische Nachrichten 2019-03, Vol.292 (3), p.540-555
Main Authors: Čech, Martin, Lachman, Dominik, Svoboda, Josef, Tinková, Magdaléna, Zemková, Kristýna
Format: Article
Language:English
Subjects:
11E12
11E25
11R04
biquadratic number field
indecomposable integer
Integers
Lower bounds
Mathematical analysis
Quadratic forms
Queuing theory
universal quadratic form
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Summary: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201800109