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arXiv · 2502.05991

Additively indecomposable quadratic forms over totally real number fields

Magdaléna Tinková·Pavlo Yatsyna
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Abstract

We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper bounds for the minimal ranks of $n$-universal quadratic forms. For $\mathbb{Q}(\sqrt{2}),~\mathbb{Q}(\sqrt{3}),~\mathbb{Q}(\sqrt{5}),~\mathbb{Q}(\sqrt{6})$, and $\mathbb{Q}(\sqrt{21})$, we classify, up to equivalence, all classical, additively indecomposable binary quadratic forms.

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Magdaléna Tinková, Pavlo Yatsyna. 2025-02-09. Additively indecomposable quadratic forms over totally real number fields. https://arxiv.org/abs/2502.05991

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