Universal quadratic forms and indecomposables over biquadratic fields | Zendy

Čech Martin | Zendy; Lachman Dominik | Zendy; Svoboda Josef | Zendy; Tinková Magdaléna | Zendy; Zemková Kristýna | Zendy

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Universal quadratic forms and indecomposables over biquadratic fields

Author(s) -

Čech Martin,

Lachman Dominik,

Svoboda Josef,

Tinková Magdaléna,

Zemková Kristýna

Publication year - 2019

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201800109

Subject(s) - indecomposable module , mathematics , quadratic equation , algebraic number , quadratic field , algebraic number field , field (mathematics) , pure mathematics , discrete mathematics , algebra over a field , mathematical analysis , quadratic function , geometry

The aim of this article is to study (additively) indecomposable algebraic integers O K of biquadratic number fields K and universal totally positive quadratic forms with coefficients in O K . 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.

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