Geodesic
On a~property of the correlation coefficient
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 562-563

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Let (4) be a two-dimensional density function, then the correlation coefficient between $\xi$ and $\eta$ is equal zero, if and only if they are independent. 
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     author = {O. V. Sarmanov},
     title = {On a~property of the correlation coefficient},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {562--563},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a16/}
}
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O. V. Sarmanov. On a~property of the correlation coefficient. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 562-563. http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a16/