Rational points in Cantor sets in the complex plane
Abstract
Let K be an imaginary quadratic field and let OK be the ring of algebraic integers of K. For α∈OK with |α|>1, define Dα=⋃n=0∞OKαn. For β∈OK with |β|>1 and a finite subset A⊂OK, define Sβ,A={∑k=1∞akβk:ak∈A ∀k∈N}. Suppose that α and β are relatively prime. In this paper, we show that if dimHSβ,A
Fields of Study & Subjects
Rings
Modules
and Algebras
Mathematical Dynamics and Fractals
Holomorphic and Operator Theory
Publication details
- Journal / source
- Acta Arithmetica
- Publication date
- 17 September 2026