Universal quadratic forms and indecomposables over biquadratic fields |
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Authors: | Martin ech,Dominik Lachman,Josef Svoboda,Magdal na Tinkov ,Kristý na Zemkov |
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Affiliation: | Martin Čech,Dominik Lachman,Josef Svoboda,Magdaléna Tinková,Kristýna Zemková |
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Abstract: | The aim of this article is to study (additively) indecomposable algebraic integers of biquadratic number fields K and universal totally positive quadratic forms with coefficients in . 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 and , a lower bound on the number of variables of a universal quadratic forms. |
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Keywords: | biquadratic number field indecomposable integer universal quadratic form 11E12 11E25 11R04 |
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