Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415576 | Journal of Number Theory | 2013 | 13 Pages |
Abstract
For β>1, a function (â )β maps each infinite word a1a2â¯âNN to a real number âi=1âai/βi. We define Î(α,β) by (sα,0â²)β where sα,0â² is a lexicographically greatest mechanical word of slope α. This paper demonstrates that the function Î enjoys devilʼs staircase-like properties. Its continuity, partial and total differentiability will be investigated. We also present a set of Î-values, in which any finite number of members are algebraically independent over the field of rationals.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
DoYong Kwon,