Equidistribution of digits in powers and Diophantine approximations

Edson de Faria; Charles Tresser

Equidistribution of digits in powers and Diophantine approximations

Dynamical Systems 2015-03-05 v2

Authors: Edson de Faria , Charles Tresser

Abstract

Given integers $a,b>1$ with $\log_b{a}$ irrational, we investigate the connection between the conjectured asymptotic equidistribution of digits in the base- $b$ expansion of $a^n$ and the (non-)Diophantine properties of the number $\theta_{a,b}=\log_b{a}$ .

Keywords

equidistribution of digits powers Diophantine approximations base-b expansion irrational numbers asymptotic distribution

Cite

@article{arxiv.1307.1505,
  title  = {Equidistribution of digits in powers and Diophantine approximations},
  author = {Edson de Faria and Charles Tresser},
  journal= {arXiv preprint arXiv:1307.1505},
  year   = {2015}
}

Comments

This paper has been withdrawn by the authors because its main result becomes trivial due to a much simpler argument

Equidistribution of digits in powers and Diophantine approximations

Abstract

Keywords

Cite

Comments

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