4 papers · 1 filter
Prescribed realisation of longest runs in continued fractions
Ying Wai Lee
Exceptional longest-run behaviour in continued fraction expansions is studied through the interaction between fixed-symbol runs and the overall longest run. For every prescribed pa…
Decomposition of real numbers into sums of Lüroth sets
Maiken Gravgaard, Ying Wai Lee
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…
Quantitative longest-run laws for partial quotients
Ying Wai Lee
Two longest-run statistics are studied: the longest run of a fixed value and the longest run over all values. Under quantitative mixing and exponential cylinder estimates for const…
Lüroth Expansions in Diophantine Approximation: Metric Properties and Conjectures
Ying Wai Lee
This paper focuses on the metric properties of Lüroth well approximable numbers, studying analogous of classical results, namely the Khintchine Theorem, the JarnÃk--Besicovitch T…