Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 3 min ago
PreprintCC BY 4.0arXiv

Transcendence of dendric beta-expansions with pure discrete spectrum

  • Jihyuk Seo
  • Wolfgang Steiner
Open at sourcePDFDOICite

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.

Related

  1. Resolvent Expansions at All Spectral Thresholds for Three-Dimensional Discrete Schrödinger Operators
    Yanhong Chen, Sisi Huang, Xiaohua Yao
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. Beta-expansions induced by general Parry polynomials and sharp iteration asymptotics of their transfer operators
    Horia D. Cornean, Ira W. Herbst, Kasper S. Sørensen
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv
  3. The height of discrete-time critical beta-splitting trees
    Heng Ma
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. The Spectrum of the Discrete Mathieu Operator with Nonreal Coupling
    Frédéric Klopp, Izak Oltman
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  5. On the Emergence of Discrete Spectrum for Weakly Disordered Schrödinger Operators
    Oleg Safronov
    arXivPreprintarXiv licenceFull textMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{seo2026transcendence,
  title = {{Transcendence of dendric beta-expansions with pure discrete spectrum}},
  author = {Jihyuk Seo and Wolfgang Steiner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00856},
  eprint = {2610.00856},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00856},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Transcendence of dendric beta-expansions with pure discrete spectrum
AU  - Jihyuk Seo
AU  - Wolfgang Steiner
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.00856
UR  - https://arxiv.org/abs/2610.00856
AB  - 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.
ER  -