Using continued fractions with prescribed period for universal quadratic forms
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.
Fields of Study & Subjects
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 14 January 2026
- Document type
- Preprint