Geodesic
Distribution of poles of rational functions of best approximation
Matematičeskie zametki, Tome 7 (1970) no. 3, pp. 289-293.

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This article describes the construction of an entire function $E(z)$ such that for any sequence $\{\overset{*}{r}_n(z)\}$ of rational functions of best approximation to $E(z)$ on the unit disc $K$, the corresponding set of poles $\{\overset{*}{\alpha}_{nk}\}$ is everywhere dense in the complement of $K$. 
@article{MZM_1970_7_3_a3,
     author = {G. A. Volkov},
     title = {Distribution of poles of rational functions of best approximation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {289--293},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_3_a3/}
}
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G. A. Volkov. Distribution of poles of rational functions of best approximation. Matematičeskie zametki, Tome 7 (1970) no. 3, pp. 289-293. http://geodesic.mathdoc.fr/item/MZM_1970_7_3_a3/