Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Rational numbers in $\times b$-invariant sets
HTML articles powered by AMS MathViewer

by Bing Li, Ruofan Li and Yufeng Wu
Proc. Amer. Math. Soc. 151 (2023), 1877-1887
DOI: https://doi.org/10.1090/proc/16278
Published electronically: February 2, 2023

Abstract:

Let $b \geq 2$ be an integer and $S$ be a finite non-empty set of primes not containing divisors of $b$. For any non-dense set $A \subseteq [0,1)$ which is invariant under $\times b$ operation, 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.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 11A63, 37E05
  • Retrieve articles in all journals with MSC (2020): 11A63, 37E05
Bibliographic Information
  • Bing Li
  • Affiliation: School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China
  • MR Author ID: 898023
  • ORCID: 0000-0003-2976-5616
  • Email: scbingli@scut.edu.cn
  • Ruofan Li
  • Affiliation: School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China
  • ORCID: 0000-0003-3842-176X
  • Email: liruofan@scut.edu.cn
  • Yufeng Wu
  • Affiliation: School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China
  • Email: yufengwu@scut.edu.cn
  • Received by editor(s): April 23, 2022
  • Received by editor(s) in revised form: July 28, 2022, and September 1, 2022
  • Published electronically: February 2, 2023
  • Additional Notes: This research was partially supported by NSFC 11671151 and 12271176.
  • Communicated by: Katrin Gelfert
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 1877-1887
  • MSC (2020): Primary 11A63, 37E05
  • DOI: https://doi.org/10.1090/proc/16278
  • MathSciNet review: 4556185