Other versions available
Dimensions of the popcorn graph
Published: 18 August 2022
Proceedings of the American Mathematical Society , Volume 150, pp 4729-4742; https://doi.org/10.1090/proc/15729
Abstract: The ‘popcorn function’ is a well-known and important example in real analysis with many interesting features. We prove that the box dimension of the graph of the popcorn function is 4/3, as well as computing the Assouad dimension and Assouad spectrum. The main ingredients include Duffin-Schaeffer type estimates from Diophantine approximation and the Chung-Erdős inequality from probability theory.
Keywords: Popcorn function / Thomae function / box dimension / Assouad dimension / Assouad spectrum
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Click here to see the statistics on "Proceedings of the American Mathematical Society" .