Geodesic
A~criterion for the algebraic independence of values of a~class of hypergeometric $E$-functions
Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 203-226

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A criterion for the irreducibility of the equation $$ \biggl\{\biggl(z\frac\partial{dz}+\lambda_1\biggr)\dotsb\biggl(z\frac\partial{dz}+\lambda_{t+l}\biggr)-z^t\biggl(z\frac\partial{dz}+\nu_1\biggr)\dotsb \biggl(z\frac\partial{dz}+\nu_l\biggr)\biggr\}(y)=0 $$ is established in the case when $l\geqslant 0$ and $t$ is odd. Arithmetical applications of this result are obtained. 
@article{SM_1991_69_1_a12,
     author = {V. Kh. Salikhov},
     title = {A~criterion for the algebraic independence of values of a~class of hypergeometric $E$-functions},
     journal = {Sbornik. Mathematics},
     pages = {203--226},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_69_1_a12/}
}
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V. Kh. Salikhov. A~criterion for the algebraic independence of values of a~class of hypergeometric $E$-functions. Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 203-226. http://geodesic.mathdoc.fr/item/SM_1991_69_1_a12/