Geodesic
The irrationality of the values of certain transcendental functions
Izvestiya. Mathematics, Tome 2 (1968) no. 1, pp. 89-104 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. G. Sprindzhuk. The irrationality of the values of certain transcendental functions. Izvestiya. Mathematics, Tome 2 (1968) no. 1, pp. 89-104. http://geodesic.mathdoc.fr/item/IM2_1968_2_1_a4/

[1] Siegel G., “Über einige Anwendungen Diophantische Approximalionen”, Abhandl. Preuss. Acad. Wiss., 1929–1930, no. 1, 1–70 | Zbl

[2] Siegel C., Transcendental numbers, Princeton, 1949 | MR

[3] Gelfond A. O., Transtsendentnye i algebraicheskie chisla, GITTL, M., 1952

[4] Trikomi F., Differentsialnye uravneniya, IL, M., 1962

[5] Matveev N. M., Metody integrirovaniya obyknovennykh differentsialnykh uravnenii, Vyssh. shkola, M., 1963

[6] Shidlovskii A. B., “O kriterii algebraicheskoi nezavisimosti znachenii odnogo klassa tselykh funktsii”, Dokl. AN SSSR, 100:2 (1955), 221–224 | Zbl

[7] Shidlovskii A. B., “O kriterii algebraicheskoi nezavisimosti znachenii odnogo klassa tselykh funktsii”, Izv. AN SSSR. Ser. matem., 23 (1959), 35–66 | Zbl

[8] Shidlovskii A. B., “O transtsendentnosti i algebraicheskoi nezavisimosti znachenii nekotorykh funktsii”, Tr. Mosk. matem. ob-va, 8 (1959), 283–320

[9] Shidlovskii A. B., “O transtsendentnosti l algebraicheskoi nezavisimosti znachenii nekotorykh $E$-funktsii”, Vestn. Mosk. un-ta, 5 (1961), 44–59 | MR

[10] Shidlovskii A. B., “O transtsendentnosti i algebraicheskoi nezavisimosti znachenii $E$-funktsii, svyazannykh lyubym chislom algebraicheskikh uravnenii v pole ratsionalnykh funktsii”, Izv. AN SSSR. Ser. matem., 26 (1962), 877–910 | Zbl

[11] Shidlovskii A. B., “Transtsendentnost znachenii nekotorykh klassov funktsii”, Litovskii matem. sb., 1966, no. 1, 129–130