Geodesic
Diophantine approximation and special Liouville numbers
Communications in Mathematics, Tome 21 (2013) no. 1, pp. 39-76.

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This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\zeta_{1},\zeta_{2},\ldots ,\zeta_{k}$. The approach relies on results on the connection between the set of all $s$-adic expansions ($s\geq 2$) of $\zeta_{1},\zeta_{2},\ldots ,\zeta_{k}$ and their associated approximation constants. As an application, explicit construction of real numbers $\zeta_{1},\zeta_{2},\ldots ,\zeta_{k}$ with prescribed approximation properties are deduced and illustrated by Matlab plots.
Classification : 11H06, 11J13, 11J81
Keywords: convex geometry; lattices; Liouville numbers; successive minima 
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     author = {Schleischitz, Johannes},
     title = {Diophantine approximation and special {Liouville} numbers},
     journal = {Communications in Mathematics},
     pages = {39--76},
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     url = {http://geodesic.mathdoc.fr/item/COMIM_2013__21_1_a3/}
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Schleischitz, Johannes. Diophantine approximation and special Liouville numbers. Communications in Mathematics, Tome 21 (2013) no. 1, pp. 39-76. http://geodesic.mathdoc.fr/item/COMIM_2013__21_1_a3/