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arXiv · 2311.16660

Bounds on the Pythagoras number and indecomposables in biquadratic fields

Magdaléna Tinková
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Abstract

We show that for all real biquadratic fields not containing $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, $\sqrt{6}$, $\sqrt{7},$ and $\sqrt{13}$, the Pythagoras number of the ring of algebraic integers is at least $6$. We will also provide an upper bound on the norm and the minimal (codifferent) trace of additively indecomposable integers in some families of these fields.

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Magdaléna Tinková. 2023-11-28. Bounds on the Pythagoras number and indecomposables in biquadratic fields. https://arxiv.org/abs/2311.16660

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