Using continued fractions with prescribed period for universal quadratic forms

Veronika Mensikova; Helena Muchova

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arXiv · 2601.09419

Using continued fractions with prescribed period for universal quadratic forms

Veronika Mensikova·Helena Muchova

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Abstract

We study the congruence classes attained by positive integers $D$ with a prescribed period of the continued fraction of $\sqrt D$. As an application, we refine the available results on large ranks of universal quadratic forms over real quadratic fields by also imposing congruence conditions on their discriminants.

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Veronika Mensikova, Helena Muchova. 2026-01-14. Using continued fractions with prescribed period for universal quadratic forms. https://arxiv.org/abs/2601.09419

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