Geodesic
Approximation of the function $|x|$ by rational functions
Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 163-171.

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We consider the problem of the approximation of the function $|x|$ by rational functions. We make more precise the best approximation estimate obtained by A. P. Bulanov. We prove that for arbitrary positive integral $n$ $$ R_n[|x|]^{-\pi\sqrt n} $$ where $A$ is an absolute constant. 
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     author = {N. S. Vyacheslavov},
     title = {Approximation of the function $|x|$ by rational functions},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a18/}
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N. S. Vyacheslavov. Approximation of the function $|x|$ by rational functions. Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 163-171. http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a18/