V. Kh. Salikhov, “A criterion for the algebraic independence of values of a class of hypergeometric <nobr>$E$</nobr>-functions”, Mat. Sb., 1990, Volume 181, Number 2,Pages <nobr>189

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A criterion for the algebraic independence of values of a class of hypergeometric $E$-functions

V. Kh. Salikhov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 511.36

MSC: 11J85, 33A35

Received: 23.05.1988