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On irrationality of the values of the functions $F(x,s)$

E. M. Nikishin


Abstract: 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.

UDC: 511.74

MSC: Primary 10F37; Secondary 10F10

Received: 25.12.1978

 English version: Mathematics of the USSR-Sbornik, 1980, 37:3, 381–388

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