Geodesic
Estimates of the number of zeros of some functions with algebraic Taylor coefficients
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 817-824.

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We prove two theorems about the number of zeros of analytic functions from certain classes that include the Siegel $E$-and $G$-functions. By using these theorems, we arrive at a new proof of the Gel'fond-Schneider theorem and improve the result that the numerical determinant does not vanish in the proof of the Shidlovskii theorem. 
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     title = {Estimates of the number of zeros of some functions with algebraic {Taylor} coefficients},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a2/}
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A. I. Galochkin. Estimates of the number of zeros of some functions with algebraic Taylor coefficients. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 817-824. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a2/

[1] Shidlovskii A. B., Transtsendentnye chisla, Nauka, M., 1987

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

[3] Kheiman U., Meromorfnye funktsii, Mir, M., 1966

[4] Zudilin V. V., “Ob otsenkakh snizu mnogochlenov ot znachenii nekotorykh tselykh funktsii”, Matem. sb., 187:12 (1996), 57–86 | MR | Zbl

[5] Chudnovsky G. V., “On some applications of diophantine approximations”, Proc. Nat. Acad. Sci. USA, 81, March (1984), 1926–1930 | DOI | MR | Zbl