A Note on Diophantine Approximation with Restricted Denominators

Chance Sanford

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arXiv · 2606.02620

A Note on Diophantine Approximation with Restricted Denominators

Chance Sanford

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Abstract

In this note we explore rational approximations to irrational numbers whose denominators are restricted to a subset of the natural numbers. We introduce a specific notion of density for such subsets and use it to establish a restricted analog of a theorem of Dirichlet's.

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Chance Sanford. 2026-05-28. A Note on Diophantine Approximation with Restricted Denominators. https://arxiv.org/abs/2606.02620

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