Sums of squares in $S$-integers

Vítězslav Kala; Pavlo Yatsyna

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arXiv · 2005.06566

Sums of squares in $S$-integers

Vítězslav Kala·Pavlo Yatsyna

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Abstract

In totally real number fields, we characterize the rings of $S$-integers (obtained by inverting a rational integer $m$) such that all their totally positive elements are represented as a sum of squares. We further obtain partial answers to the question: when are all the totally positive algebraic integers that are divisible by $m$ represented as a sum of squares?

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Vítězslav Kala, Pavlo Yatsyna. 2020-05-13. Sums of squares in $S$-integers. https://arxiv.org/abs/2005.06566

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