English, Article, Journal or magazine article edition: A Singular Function and its Relation with the Number Systems Involved in its Definition Jaume Paradís; Pelegrí Viader; Lluís Bibiloni

User activity

Share to:
 
Bookmark: http://trove.nla.gov.au/version/154664
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • A Singular Function and its Relation with the Number Systems Involved in its Definition
Author
  • Jaume Paradís
  • Pelegrí Viader
  • Lluís Bibiloni
Physical Description
  • preprint
Notes
  • Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =​5.31972, and ?'(x) exists then ?'(x)=​0. In the same way, if the same average is less than k**=​2 log2(F), where F is the golden ratio, then ?'(x)=​infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.
  • Singular function, number systems, metric number theory
  • RePEc:upf:upfgen:378
Language
  • English
Contributed by
OAIster

Get this edition

Other links

  • 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