Geodesic
Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers
Izvestiya. Mathematics, Tome 11 (1977) no. 2, pp. 239-270 
Yu. V. Nesterenko. Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers. Izvestiya. Mathematics, Tome 11 (1977) no. 2, pp. 239-270. http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

By the use of estimates for the multiplicities of the zeros of polynomials in certain fixed functions, an estimate is proved for the measure of algebraic independence of the values of the functions which is effective in the degree and height. Bibliography: 10 titles.

[1] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Mir, M., 1972 | MR

[2] Van-der-Varden B. L., Sovremennaya algebra, t. II, Gostekhizdat, M., L., 1947

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

[4] Hurwitz A., “Über die Trägheitsformen eines algebraischen Moduls”, Annali di Matematica (Milano), ser. 3, 20 (1913), 113–151 | DOI | Zbl

[5] Zarisskii O., Samyuel P., Kommutativnaya algebra, t. I, II, IL, M., 1963

[6] Siegel C. L., “Über einige Anwendugnen Diophantischer Approximationen”, Abh. Preuss. Akad. Wiss., Phys.-Math. Kl., 1 (1929), 1–70 | Zbl

[7] Lang S., “A transcendence measure for $E$-function”, Math., 9 (1962), 157–161 | MR | Zbl

[8] Nesterenko Yu. V., “Ob algebraicheskoi zavisimosti komponent reshenii sistemy lineinykh differentsialnykh uravnenii”, Izv. AN SSSR. Ser. matem., 38 (1974), 495–512 | MR | Zbl

[9] Shafarevich I. R., Osnovy algebraicheskoi geometrii, Nauka, M., 1972 | MR | Zbl

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