Abstract:
The paper presents several theorems on the linear and algebraic independence of the values at algebraic points of the set of E-functions related by algebraic equations over the field of rational functions, as well as some estimates of the absolute values of polynomials with integer coefficients in the values of such functions. The results are obtained by using the properties of ideals in the ring of polynomials of several variables formed by equations relating the above functions over the field of rational functions.
Citation:
A. B. Shidlovskii, “Properties of Algebraic Equations on the Set of E-Functions over the Field of Rational Functions”, Mat. Zametki, 68:5 (2000), 761–770; Math. Notes, 68:5 (2000), 644–651
\Bibitem{Shi00}
\by A.~B.~Shidlovskii
\paper Properties of Algebraic Equations on the Set of $E$-Functions over the Field of Rational Functions
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 5
\pages 761--770
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\crossref{https://doi.org/10.4213/mzm996}
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\zmath{https://zbmath.org/?q=an:1012.11064}
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\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 5
\pages 644--651
\crossref{https://doi.org/10.1023/A:1026679809925}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000166684000012}
Linking options:
https://www.mathnet.ru/eng/mzm996
https://doi.org/10.4213/mzm996
https://www.mathnet.ru/eng/mzm/v68/i5/p761
This publication is cited in the following 1 articles:
V. V. Kozlov, O. B. Lupanov, Yu. V. Nesterenko, M. K. Potapov, V. A. Sadovnichii, P. L. Ul'yanov, “Andrei Borisovich Shidlovskii (on his 90th birthday)”, Russian Math. Surveys, 61:2 (2006), 379–386
Citation in format AMSBIB
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