Tan–Zhou's Hausdorff-dimension conjecture for Lüroth approximation sets
Tan–Zhou's Hausdorff-dimension conjecture for Lüroth approximation sets
Let be the set of points defined by the Lüroth approximation condition associated with a function , and let denote the corresponding lower approximation exponent. Tan–Zhou's conjecture. For every function ,
This is proposed as an analogue of a result of Dodson. The statement is false without a monotonicity assumption, as the paper gives examples with the same value of but Hausdorff dimension zero; the monotone version is therefore the surviving open conjecture.
Sources & referencesView supporting material
Primary source
Ying Wai Lee, “Lüroth Expansions in Diophantine Approximation: Metric Properties and Conjectures”, arXiv:2502.08408 (2025).
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