Liouville Numbers

1980 ◽  
pp. 6-9
Author(s):  
John C. Oxtoby
Keyword(s):  
Liouville Numbers

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

On the exact Hausdorff dimension of the set of Liouville numbers. II

2005 ◽  
Vol 119 (2) ◽  
pp. 217-224 ◽  
Author(s):  
L. Olsen ◽  
Dave L. Renfro
Keyword(s):  
Hausdorff Dimension ◽  
Liouville Numbers

scholarly journals Liouville numbers and Schanuel’s Conjecture

2014 ◽  
Vol 102 (1) ◽  
pp. 59-70 ◽  
Author(s):  
K. Senthil Kumar ◽  
R. Thangadurai ◽  
M. Waldschmidt
Keyword(s):  
Liouville Numbers ◽  
Schanuel's Conjecture

scholarly journals ON MAHLER’S -ADIC -NUMBERS

2012 ◽  
Vol 88 (1) ◽  
pp. 44-50
Author(s):  
GÜLCAN KEKEÇ
Keyword(s):  
Algebraic Numbers ◽  
Liouville Numbers

AbstractThe aim of this work is to adapt a construction of the so-called $U_{m}$-numbers ($m\gt 1$), which are extended Liouville numbers with respect to algebraic numbers of degree $m$ but not with respect to algebraic numbers of degree less than $m$, to the $p$-adic frame.

scholarly journals On approximation constants for Liouville numbers

2015 ◽  
Vol 50 (2) ◽  
pp. 349-361
Author(s):  
Johannes Schleischitz ◽  
Keyword(s):  
Liouville Numbers
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