This article is cited in 5 papers

The irrationality of the values of certain transcendental functions

V. G. Sprindzhuk


Abstract: In this paper we prove that an entire transcendental function, satisfying a first-order linear differential equation with polynomial coefficients and belonging to a more extensive class than Siegel's class of $E$-functions, assumes algebraic values of bounded degree only at a finite number of algebraic points of bounded degree.

UDC: 511

MSC: 34M15, 33C60, 34A30

Received: 28.02.1967

 English version: Mathematics of the USSR-Izvestiya, 1968, 2:1, 89–104

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