4 papers
How many points contain homothetic copies in their Hurwitz continued fraction expansion?
Yuto Nakajima, Hiroki Takahasi
We prove that the set of complex irrationals whose partial quotients in their Hurwitz continued fraction expansion are naturally regarded as subsets of and contain in…
Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions
Yuto Nakajima, Hiroki Takahasi, Baowei Wang
Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a…
A problem of Hirst for the Hurwitz continued fraction and the Hausdorff dimension of sets with restricted slowly growing digits
Yuto Nakajima, Hiroki Takahasi
We address the problem of determining the Hausdorff dimension of sets consisting of complex irrationals whose complex continued fraction digits satisfy prescribed restrictions and…
Density combinatorics theorems in fractal dimension theory of continued fractions
Yuto Nakajima, Hiroki Takahasi
We build a bridge from density combinatorics to dimension theory of continued fractions. We establish a fractal transference principle that transfers common properties of subsets o…