Geodesic
Transcendence of the values of $E$-functions that are solutions of second order linear differential equations
Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 63-71 
A. B. Shidlovskii. Transcendence of the values of $E$-functions that are solutions of second order linear differential equations. Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 63-71. http://geodesic.mathdoc.fr/item/SM_1994_79_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The solution of the problem of transcendence of the values at algebraic points of $E$-functions that are solutions of second order homogeneous linear differential equations with coefficient in $\mathbb{C}(z)$ is completed in this article.

[1] Siegel C. L., “Über einige Anwendungen Diophantischer Approximationen”, Abh. Preuss. Wiss. Phys. Math. Kl., 1929–1930, no. 1, 1–70 | Zbl

[2] Siegel C. L., Transcendental numbers, Princenton University Press, 1949 | MR

[3] Shidlovskii A. B., “O kriterii algebraicheskoi nezavisimosti znachenii odnogo klassa tselykh funktsii”, DAN SSSR, 100:2 (1955), 221–224 ; Известия АН СССР. Серия матем., 23:1 (1959), 35–66 | MR | Zbl | MR | Zbl

[4] Shidlovskii A. B., “O transtsendentnosti i algebraicheskoi nezavisimosti znachenii $\operatorname {E}$-funktsii, svyazannykh lyubym chislom algebraicheskikh uravnenii v pole ratsionalnykh funktsii”, Izv. AN SSSR. Ser matem., 26:6 (1962), 877–910 | MR | Zbl

[5] Valter de Gruyter, Berlin–New York, 1989 | MR

[6] Shidlovskii A. B., “Ob odnom kriterii algebraicheskoi nezavisimosti znachenii $\operatorname {E}$-funktsii v algebraicheskikh tochkakh”, Vestn. MGU. Ser. 1. Matematika, mekhanika, 1989, no. 6, 17–21 | MR

[7] Shidlovskii A. B., “Ob algebraicheskoi nezavisimosti znachenii $\operatorname {E}$-funktsii”, UMN, 46:4 (1991), 175–176 | MR