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Can I read The Derivative of Minkowski's ?(x) Function on EtoBox?
The Derivative of Minkowski's ?(x) Function by J. Paradı́s; P. Viader; L. Bibiloni is a Mathematics article available to read on EtoBox.
What is The Derivative of Minkowski's ?(x) Function about?
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 enables us to prove that its derivative, when it exists in a wide sense, 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 Ž . Ž . k s 5.31972, and ?Ј x exists, then ?Ј x s 0. In the same way, if the same average Ž . is less than k s 2 log ⌽, where ⌽ is the golden ratio, then ?Ј x s ρ. Finally 2 some results are presented concerning metric properties of continued fractions and alternated dyadic expansions.
Who reads The Derivative of Minkowski's ?(x) Function?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- J. Paradı́s; P. Viader; L. Bibiloni
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)
- Published
- 2001
- Language
- EN
- Field
- Mathematics (Physical Sciences)