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 Mat. Zametki, 1997, Volume 61, Issue 6, Pages 817–824 (Mi mz1566)

Estimates of the number of zeros of some functions with algebraic Taylor coefficients

A. I. Galochkin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

DOI: https://doi.org/10.4213/mzm1566

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English version:
Mathematical Notes, 1997, 61:6, 687–692

Bibliographic databases:

UDC: 511.36

Citation: A. I. Galochkin, “Estimates of the number of zeros of some functions with algebraic Taylor coefficients”, Mat. Zametki, 61:6 (1997), 817–824; Math. Notes, 61:6 (1997), 687–692

Citation in format AMSBIB
\Bibitem{Gal97} \by A.~I.~Galochkin \paper Estimates of the number of zeros of some functions with algebraic Taylor coefficients \jour Mat. Zametki \yr 1997 \vol 61 \issue 6 \pages 817--824 \mathnet{http://mi.mathnet.ru/mz1566} \crossref{https://doi.org/10.4213/mzm1566} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629789} \zmath{https://zbmath.org/?q=an:0968.11028} \transl \jour Math. Notes \yr 1997 \vol 61 \issue 6 \pages 687--692 \crossref{https://doi.org/10.1007/BF02361210} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YE52200022} 

• http://mi.mathnet.ru/eng/mz1566
• https://doi.org/10.4213/mzm1566
• http://mi.mathnet.ru/eng/mz/v61/i6/p817

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This publication is cited in the following articles:
1. W. V. Zudilin, “On the algebraic structure of functional matrices of special form”, Math. Notes, 60:6 (1996), 642–648
2. Fischler S., “Shidlovsky'S Multiplicity Estimate and Irrationality of Zeta Values”, J. Aust. Math. Soc., 105:2 (2018), 145–172
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