Universal Quadratic Forms and Indecomposables over Biquadratic Fields
| Autor: | Čech, Martin, Lachman, Dominik, Svoboda, Josef, Tinková, Magdaléna, Zemková, Kristýna |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | The aim of this article is to study (additively) indecomposable algebraic integers $\mathcal O_K$ of biquadratic number fields $K$ and universal totally positive quadratic forms with coefficients in $\mathcal O_K$. 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 $\mathbb{Q}(\sqrt{2}, \sqrt{3})$ and $\mathbb{Q}(\sqrt{6}, \sqrt{19})$, a lower bound on the number of variables of a universal quadratic forms, verifying Kitaoka's conjecture. Comment: 14 pages, comments are welcome |
| Databáze: | arXiv |
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