Work

Transcendence of dendric beta-expansions with pure discrete spectrum

Year: 2026

Type: preprint

Abstract: We prove the transcendence of numbers that have $β$-expansions (in algebraic bases $β$) belonging to dendric shifts with pure discrete spectrum, under combinatorial conditions on their directive sequences of substitutions. This includes Arnoux-Rauzy sequences on arbitrary alphabets and Cassaigne-Selmer sequences. The proof uses Rauzy fractals and the subspace theorem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.00856

Authors: Seo, Jihyuk, Steiner, Wolfgang

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Austrian Science Fund

Awards: Symbolic dynamics and arithmetic expansions, Inside zero entropy systems, G7080048889, Symbolic dynamics and arithmetic expansions

OpenAlex ID: W7216538846

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