2009, English, Article edition: Words and Transcendence Waldschmidt, Michel

User activity

Share to:
 
Bookmark: http://trove.nla.gov.au/version/205712
Physical Description
  • text
Published
  • HAL - CCSD
  • 2009
Language
  • English

Edition details

Title
  • Words and Transcendence
Author
  • Waldschmidt, Michel
Published
  • HAL - CCSD
  • 2009
Physical Description
  • text
Subjects
Notes
  • Is it possible to distinguish algebraic from transcendental real numbers by considering the $b$-ary expansion in some base $b\ge2$? In 1950, \'E. Borel suggested that the answer is no and that for any real irrational algebraic number $x$ and for any base $g\ge2$, the $g$-ary expansion of $x$ should satisfy some of the laws that are shared by almost all numbers. For instance, the frequency where a given finite sequence of digits occurs should depend only on the base and on the length of the sequence. We are very far from such a goal: there is no explicitly known example of a triple $(g,a,x)$, where $g\ge3$ is an integer, $a$ a digit in $\{0,\ldots,g-1\}$ and $x$ a real irrational algebraic number, for which one can claim that the digit $a$ occurs infinitely often in the $g$-ary expansion of~$x$. Hence there is a huge gap between the established theory and the expected state of the art. However, some progress has been made recently, thanks mainly to clever use of Schmidt's subspace theorem. We review some of these results.
  • HAL:hal-00407221, version 1
  • HAL:http:/​/​hal.archives-ouvertes.fr/​hal-00407221/​en/​
Language
  • English
Contributed by
OAIster

Get this edition

  • Set up My libraries

    How do I set up "My libraries"?

    In order to set up a list of libraries that you have access to, you must first login or sign up. Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen.

  • All (1)
  • Unknown (1)
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.

User activity


e.g. test cricket, Perth (WA), "Parkes, Henry"

Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes.

Be the first to add a tag for this edition

Be the first to add this to a list

Comments and reviews

What are comments? Add a comment

No user comments or reviews for this version

Add a comment