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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received: 17.05.1996

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
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\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}


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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Fischler S., “Shidlovsky'S Multiplicity Estimate and Irrationality of Zeta Values”, J. Aust. Math. Soc., 105:2 (2018), 145–172  crossref  mathscinet  zmath  isi  scopus
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