Rational points in Cantor sets and spectral eigenvalue problem for self-similar spectral measures
Year: 2025
Type: article
Abstract: Given q ∈ ℕ ≥ 3 {q\in\mathbb{N}_{\geq 3}} and a finite set A ⊂ ℚ {A\subset\mathbb{Q}} , let K ( q , A ) = { ∑ i = 1 ∞ a i q i : a i ∈ A for all i ∈ ℕ } . K(q,A)=\Bigg{\{}\sum_{i=1}^{\infty}\frac{a_{i}}{q^{i}}:a_{i}\in A\text{ for % all }i\in\mathbb{N}\Bigg{\}}. For p ∈ ℕ ≥ 2 {p\in\mathbb{N}_{\geq 2}} let D p ⊂ ℝ {D_{p}\subset\mathbb{R}} be the set of all rational numbers having a finite p -ary expansion. We show in this paper that for p ∈ ℕ ≥ 2 {p\in\mathbb{N}_{\geq 2}} with gcd ( p , q ) = 1 {\gcd(p,q)=1} , the intersection
Source: Forum Mathematicum
Authors: Derong Kong, Kun Li, Zhiqiang Wang
Institution: Chongqing University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2144897201, G3728004676, G6035935725
OpenAlex ID: W7117367661