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math.NT2026
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…
math.NT2025
Hausdorff dimension of intersections between the Jarník sets and Diophantine fractals
Hiroki Takahasi
The irrationality exponent of a real number measures how well that number can be approximated by rationals. Real numbers with irrationality exponent strictly greater than are t…
math.NT2025
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…