Critical bases for ternary alphabets

Vilmos Komornik; Marco Pedicini

Critical bases for ternary alphabets

Number Theory 2016-05-31 v1

Authors: Vilmos Komornik , Marco Pedicini

Abstract

Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant $q'\approx1.78723$ in non-integer base expansions on two-letter alphabets: in bases $1<q<q'$ only countably numbers have unique expansions, while for $q\ge q'$ there is a continuum of such numbers. We investigate the analogous question for ternary alphabets.

Keywords

univoque expansions

Cite

@article{arxiv.1605.08990,
  title  = {Critical bases for ternary alphabets},
  author = {Vilmos Komornik and Marco Pedicini},
  journal= {arXiv preprint arXiv:1605.08990},
  year   = {2016}
}

Comments

27 pages, 9 figures

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