Representing multiples of $m$ in real quadratic fields as sums of squares

DOI10.1016/J.JNT.2022.09.011arXiv2105.11423MaRDI QIDQ6368406

Martin Raška

Publication date: 24 May 2021

Abstract: We study real quadratic fields $mathbbQ(sqrtD)$ such that, for a given rational integer $m$, all $m$-multiples of totally positive integers are sums of squares. We prove quite sharp necessary and sufficient conditions for this to happen. Further, we give a fast algorithm that solves this question for specific $m$, $D$ and we give complete results for $mleq5000$.

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Quadratic extensions (11R11) Quadratic forms over global rings and fields (11E12) Totally real fields (11R80)

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