This article is cited in 1 paper

On the algebraic irreducibility of the set of linear differential equations

V. Kh. Salikhov


Abstract: The set of linear differential equations of prime order with coefficients in $\mathbf C(z)$ is shown to be algebraically irreducible. This result is used to prove that the values of hypergeometric $E$-functions at the set of algebraic points are algebraically independent.
Bibliography: 15 titles.

UDC: 511.8

MSC: Primary 34A30, 11J85; Secondary 33A35

Received: 11.05.1983

 English version: Mathematics of the USSR-Izvestiya, 1986, 26:1, 185–200

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