The distribution of rational numbers on Cantor's middle thirds set

2019/09/03 by Rahm, Alexander, Solomon, Noam, Trauthwein, Tara +1 · 1 citation
#11J99 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.01198

Abstract

We give a heuristic for the number of reduced rationals on Cantor's middle thirds set, with a fixed bound on the denominator. We also describe extensive numerical computations supporting this heuristic.

Cited by

• Gaussian rational numbers in Cantor sets in the complex plane

Related

• Counting rationals and diophantine approximation in missing-digit Cantor sets
• Metric Diophantine approximation on the middle-third Cantor set
• Approximating elements of the middle third Cantor set with dyadic rationals
• On the sum of squares of middle-third Cantor set
• Sums of powers, and products of elements of the middle third Cantor set