Using continued fractions with prescribed period for universal quadratic forms

Veronika Mensikova; Helena Muchova

Using continued fractions with prescribed period for universal quadratic forms

Number Theory 2026-01-15 v1

Authors: Veronika Mensikova , Helena Muchova

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.

Keywords

continued fractions quadratic forms class number of quadratic fields

Cite

@article{arxiv.2601.09419,
  title  = {Using continued fractions with prescribed period for universal quadratic forms},
  author = {Veronika Mensikova and Helena Muchova},
  journal= {arXiv preprint arXiv:2601.09419},
  year   = {2026}
}

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8 pages

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