Abstract
We prove two theorems about the number of zeros of analytic functions from certain classes that include the SiegelE-andG-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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References
A. B. Shidlovskii,Transcendental Numbers [in Russian], Nauka, Moscow (1987); English translation: Walter de Gruyte Berlin-New York (1989).
C. L. Siegel, “Über einige Anwendungen diophantischer Approximationen,”Abh. Preuss. Wiss. Phys.-Math. Kl., No. 1, 1–70 (1929–1930).
W. Hayman,Meromorphic Functions, Oxford (1964).
V. V. Zudilin, “On lower bounds for polynomials of values of some entire functions,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],187, No. 12, 57–86 (1996).
G. V. Chudnovsky, “On some applications of Diophantine approximations,”Proc. Nat. Acad. Sci. USA,81, 1926–2930 (1984).
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Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 817–824, June, 1997.
Translated by M. A. Shishkova
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Galochkin, A.I. Estimates of the number of zeros of some functions with algebraic Taylor coefficients. Math Notes 61, 687–692 (1997). https://doi.org/10.1007/BF02361210
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DOI: https://doi.org/10.1007/BF02361210