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

2021/05/24 by Raška, Martin
#11E25 #11R11 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2105.11423

Abstract

We study real quadratic fields ℚ(√(D)) 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 m ≤ 5000.

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