A property of algebraic univoque numbers

2006/12/20 by Martijn de Vries, de Vries, M.
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary: 11A63 #Secondary:11B83

paper · pdf · doi:10.48550/arxiv.math/0612603

openalex publication_date 2006/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the set \uu of real numbers q ≥ 1 for which only one sequence (c_i) of integers 0 ≤ c_i ≤ q satisfies the equality ∑_i=1^∞ c_i q^-i = 1. In this note we show that the set of algebraic numbers in \uu is dense in the closure \uuu of \uu.

Citations

• Representations for real numbers and their ergodic properties

Related

• Unique expansions of real numbers
• Topology of univoque sets in real base expansions
• A two-dimensional univoque set
• Topology of univoque sets in double-base expansions
• Algebraic sums and products of univoque bases