Geodesic
On differential irreducibility of a class of differential equations
Izvestiya. Mathematics, Tome 16 (1981) no. 1, pp. 165-189 
V. Kh. Salikhov. On differential irreducibility of a class of differential equations. Izvestiya. Mathematics, Tome 16 (1981) no. 1, pp. 165-189. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper a method is developed for proving algebraic independence of the solutions of linear differential equations. The result is applied to prove algebraic independence of the values at an algebraic point of a class of $E$-functions. Bibliography: 9 titles.

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

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

[3] Siegel C. L., “Über einige Anwendungen Diophantische Approximationen”, Abh. Preuss. Akad. Wiss., Phys.-math., 1 (1929), 1–70 | Zbl

[4] Oleinikov V. A., “O transtsendentnosti i algebraicheskoi nezavisimosti znachenii nekotorykh tselykh funktsii”, Izv. AN SSSR. Ser. matem., 32 (1968), 63–92 | MR | Zbl

[5] Oleinikov V. A., “Algebraicheskie funktsii s razdelennymi osobennostyami”, Izv. AN SSSR. Ser. matem., 35 (1971), 1294–1315 | MR | Zbl

[6] Belogrivov I. I., “O transtsendentnosti i algebraicheskoi nezavisimosti nekotorykh gipergeometricheskikh $E$-funktsii”, Dokl. AN SSSR, 174:2 (1967), 267–270 | MR | Zbl

[7] Nesterenko Yu. V., “Ob algebraicheskoi nezavisimosti znachenii $E$-funktsii, udovletvoryayuschikh lineinym neodnorodnym differentsialnym uravneniyam”, Matem. zametki, 5:5 (1969), 587–598 | MR | Zbl

[8] Salikhov V. X., “O differentsialnoi neprivodimosti odnogo klassa differentsialnykh uravnenii”, Dokl. AN SSSR, 235:1 (1977), 30–33 | MR | Zbl

[9] Chebotarev N. G., Teoriya algebraicheskikh funktsii, Gostekhizdat, M., 1948