Geodesic
On irrationality of the values of the functions $F(x,s)$
Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 381-388 
E. M. Nikishin. On irrationality of the values of the functions $F(x,s)$. Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 381-388. http://geodesic.mathdoc.fr/item/SM_1980_37_3_a5/
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     title = {On irrationality of the values of the functions $F(x,s)$},
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     volume = {37},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/SM_1980_37_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper gives a proof of a theorem on the linear independence over $\mathbf Q$ of values of functions $F(x,s)=\sum_{n=1}^\infty\frac{x^n}{n^s}$, where $x$ is a rational number whose numerator and denominator satisfy a certain relation. Bibliography: 1 title.

[1] A. I. Galochkin, “Otsenki snizu mnogochlenov ot znachenii analiticheskikh funktsii odnogo klassa”, Matem. sb., 95(137) (1974), 396–417 | Zbl