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arXiv · 2206.12345

Some dynamics in real quadratic fields with applications to inhomogeneous minima

Nick Ramsey
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Abstract

Let $K$ be a real quadratic field. We use a symbolic coding of the action of a fundamental unit on the real $2$-torus associated to $K$ to study the family of subsets $X_t$ of norm distance $\geq t$ from the origin. As an application, we prove that inhomogeneous spectrum of $K$ contains a dense set of elements of $K$, and conclude that all isolated inhomogeneous minima lie in $K$.

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Nick Ramsey. 2022-06-24. Some dynamics in real quadratic fields with applications to inhomogeneous minima. https://arxiv.org/abs/2206.12345

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