Rational numbers in $\times b$-invariant sets

Abstract: Let $b \ge 2$ be an integer and $S$ be a finite non-empty set of primes not containing divisors of $b$. For any $\times b$-invariant, non-dense subset $A$ of $[0,1)$, we prove the finiteness of rational numbers in $A$ whose denominators can only be divided by primes in $S$. A quantitative result on the largest prime divisors of the denominators of rational numbers in $A$ is also obtained. This is joint work with Bing Li and Yufeng Wu.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

---

One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

For questions or subscribing to the mailing list, contact the organisers at numeration@irif.fr

---