Algebraic Irrational Binary Numbers Cannot Be Fixed Points of Non-trivial Constant Length or Primitive Morphisms

  title={Algebraic Irrational Binary Numbers Cannot Be Fixed Points of Non-trivial Constant Length or Primitive Morphisms},
  author={Jean-Paul Allouche and Luca Q. Zamboni},
How random are the digits of an algebraic irrational number in a given base? A common conjectured answer to this vague question is that these digits are ``really random.'' For example, define a normal number in base k 2 to be a real number x such that, for each integer d 1, each block of length d occurs in the k-ary expansion of x with frequency 1 k. A widely believed conjecture is that an algebraic irrational number is a normal number in each base k 2. This conjecture is open and seems really… CONTINUE READING

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Arithmetische Eigenschaften der Lo sungen einer Klasse von Funktionalgleichungen

  • K. Mahler
  • Math. Annalen
  • 1929
Highly Influential
6 Excerpts

Champernowne, The construction of decimals normal in the scale of ten

  • D G.
  • J. London Math. Soc
  • 1933
Highly Influential
3 Excerpts

Transcendence of numbers with a low complexity expansion

  • S. Ferenczi, C. Mauduit
  • J. Number Theory
  • 1997
3 Excerpts

 sungen einer Klasse von Funktionalgleichungen , Math

  • Arithmetische Eigenschaften der Lo
  • J . Reine Angew . Math .
  • 1988

Arithmetic properties of automata: regular sequences

  • J. H. Loxton, A. van der Poorten
  • J. Reine Angew. Math
  • 1988
1 Excerpt

lec, ``Substitution Dynamical Systems Spectral Analysis,'' Lecture Notes in Mathematics, Vol

  • M. Queff
  • 1294, Springer-Verlag,
  • 1987
1 Excerpt

e bold, ``Proprie te s combinatoires des mots infinis engendre s par certains morphismes,'' The se de troise me cycle, Universite P

  • P. Se
  • et M. Curie, Institut de Programmation, Paris,
  • 1985
2 Excerpts

U ber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Norske vid

  • A. Thue
  • Selsk. Skr. Mat. Nat. Kl. 1 (1912), 1 67…
  • 1977
1 Excerpt

``Lectures on diophantine approximations, Part I: g-adic numbers and Roth's theorem,'

  • K. Mahler
  • University of Notre Dame,
  • 1961
2 Excerpts

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