7 citations · 42 across the 23 of their papers we have counts for
6 papers · 1 filter
On the expansions of real numbers in two integer bases
Yann Bugeaud, Dong Han Kim
Let and be multiplicatively independent positive integers. We establish that the -ary expansion and the -ary expansion of an irrational real number, viewed as infinit…
Zero-one law of Hausdorff dimensions of the recurrent sets
Dong Han Kim, Bing Li
Let be the one-sided shift space with symbols and be the first return time of to the -th cylinder containing . Denote $$E^φ_{α,β}=\left\{x\inΣ:…
On the -ary expansions of and
Yann Bugeaud, Dong Han Kim
Let be an integer and an irrational real number. We prove that, if the irrationality exponent of is equal to or slightly greater than , then the -ary ex…
A new complexity function, repetitions in Sturmian words, and irrationality exponents of Sturmian numbers
Yann Bugeaud, Dong Han Kim
We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest second occurrence time of a factor of an infinite word. We charact…
Dirichlet uniformly well-approximated numbers
Dong Han Kim, Lingmin Liao
Fix an irrational number . For a real number , consider the numbers satisfying that for all large number , there exists an integer , such that $\|nθ-y…
On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation
Michael Fuchs, Dong Han Kim
We give a sufficient and necessary condition such that for almost all \[ \|nθ-s\|<ψ(n)\qquad\text{for infinitely many}\ n\in{\mathbb N}, \] where is fixed and…