# at which rational points does the Hypergeometric function take rational values

A generic example is ${}_2 F_1(\frac{1}{3},\frac{2}{3},\frac{6}{5};\frac{27}{32})=\frac{8}{5}$. So my question: Is there any description of the set of rational points at which the hypergeometric function ${}_m F_n$ takes rational values?

The references to the literature where a lot of such examples listed are apreciated very much too.

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A classical problem is to determine the cases when ${}_mF_n$ is an algebraic/rational function (this automatically implies the algebraicity of the values at algebraic points). This question was addressed in several papers by F. Beukers and his coauthors (Paula Cohen-Tretkoff is one of them). A general statement about algebraicity is in the Beukers-Heckman 1989 paper but you may find it as Theorem 1.3 in arxiv.org/abs/0812.1134 . –  Wadim Zudilin Jun 22 '10 at 14:14