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arXiv · 2404.01538

An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms

Christian Porter
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Abstract

In this paper, we revisit the theory of perfect unary forms over real quadratic fields. Specifically, we deduce an infinite family of real quadratic fields $\mathbb{Q}(\sqrt{d})$ when $d=2$ or $3$ mod $4$, such that there are three classes of perfect unary forms up to homothety and equivalence. This work, along with the work in \cite{unitred}, seems to suggest that the number of classes of perfect unary forms is related to the fundamental unit of $K$.

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Christian Porter. 2024-04-02. An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms. https://arxiv.org/abs/2404.01538

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