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arXiv · 2506.12513

Decomposition of real numbers into sums of Lüroth sets

Maiken Gravgaard·Ying Wai Lee
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Abstract

We study the decomposition of real numbers into sums of Lüroth sets, which are defined by numbers whose Lüroth expansions have prescribed digit constraints. We establish several results on the congruence modulo 1 of sums of Lüroth sets, including summands with digits bounded above, below, and combinations of the two. We also analyse the Hausdorff dimension of Lüroth sets and their sums. The results extend classical findings on continued fractions to Lüroth expansions.

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Maiken Gravgaard, Ying Wai Lee. 2026-02-17. Decomposition of real numbers into sums of Lüroth sets. https://arxiv.org/abs/2506.12513

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