Decomposition of real numbers into sums of Lüroth sets
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 analyze the Hausdorff dimension of Lüroth sets and their sums. The results extend classical findings on continued fractions to Lüroth expansions.
Fields of Study & Subjects
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 22
- Issue
- 08
- Pages
- 1931–1968
- Publication date
- 8 May 2026
- Language
- EN