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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 3(7), Pages 339–365 (Mi msb3212)  

This article is cited in 9 scientific papers (total in 9 papers)

Arithmetic properties of the values of a class of analytic functions

M. S. Nurmagomedov


Abstract: In this paper conditions are established under which the values of the given set of $G$-functions at points of an imaginary quadratic field $I$ sufficiently small in modulus are not connected by a linear equation or an equation of degree $N$ with integral coefficients in $I$ no larger than $H$ in modulus. The modulus of the corresponding linear form and the modulus of a polynomial in the values of the $G$-functions are also estimated.
Bilbiography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:3, 329–357

Bibliographic databases:

UDC: 517.53+511.9
MSC: Primary 10F35; Secondary 30A64
Received: 11.06.1970

Citation: M. S. Nurmagomedov, “Arithmetic properties of the values of a class of analytic functions”, Mat. Sb. (N.S.), 85(127):3(7) (1971), 339–365; Math. USSR-Sb., 14:3 (1971), 329–357

Citation in format AMSBIB
\Bibitem{Nur71}
\by M.~S.~Nurmagomedov
\paper Arithmetic properties of the values of a~class of analytic functions
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 3(7)
\pages 339--365
\mathnet{http://mi.mathnet.ru/msb3212}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=282928}
\zmath{https://zbmath.org/?q=an:0225.10037}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 3
\pages 329--357
\crossref{https://doi.org/10.1070/SM1971v014n03ABEH002620}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Galochkin, “Otsenki snizu mnogochlenov ot neskolkikh logarifmov algebraicheskikh chisel, blizkikh k edinitse”, UMN, 28:2(170) (1973), 235–235  mathnet  mathscinet  zmath
    2. A. I. Galochkin, “Estimates from below of polynomials in the values of analytic functions of a certain class”, Math. USSR-Sb., 24:3 (1974), 385–407  mathnet  crossref  mathscinet  zmath
    3. V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. E. M. Matveev, “Estimates for linear forms in values of $G$-functions and their applications to the solution of Diophantine equations”, Russian Math. Surveys, 36:2 (1981), 183–184  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. E. M. Matveev, “Linear forms in the values of $G$-functions, and Diophantine equations”, Math. USSR-Sb., 45:3 (1983), 379–396  mathnet  crossref  mathscinet  zmath
    6. Nguyen Tien Tai, “On estimates for the orders of zeros of polynomials in analytic functions and their application to estimates for the relative transcendence measure of values of $E$-functions”, Math. USSR-Sb., 48:1 (1984), 111–140  mathnet  crossref  mathscinet  zmath
    7. Xu Guangshan, “On the arithmetic properties of the values ofG-functions”, Acta Math Sinica, 1:2 (1985), 141  crossref  mathscinet  zmath
    8. W. V. Zudilin, “On a measure of irrationality for values of $G$-functions”, Izv. Math., 60:1 (1996), 91–118  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. W. V. Zudilin, “Cancellation of factorials”, Sb. Math., 192:8 (2001), 1181–1207  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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