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Mat. Sb. (N.S.), 1984, Volume 124(166), Number 3(7), Pages 416–430 (Mi msb2059)  

This article is cited in 7 scientific papers (total in 7 papers)

On estimates, unimprovable with respect to height, of some linear forms

A. I. Galochkin


Abstract: Lower and upper bounds that differ from each other only by a constant factor are obtained for linear forms in values of the function
$$ \psi(z)=\sum_{\nu=0}^\infty\frac{z^\nu}{b^{(s+1)\nu}\nu! [\lambda_1+1,\nu]…[\lambda_s+1,\nu]}, $$
$[\lambda+1,\nu]=(\lambda+1)…(\lambda+\nu)$, $[\lambda+1,0]=1$ and its $s$ successive derivatives at the point $z=\frac1b$ under the condition that $a,b$ and $a\lambda_1,…,a\lambda_s$ are integers in some imaginary quadratic field.
Bibliography: 9 titles.

Full text: PDF file (652 kB)
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English version:
Mathematics of the USSR-Sbornik, 1985, 52:2, 407–421

Bibliographic databases:

UDC: 511.8
MSC: 10C02, 10F10
Received: 09.03.1983

Citation: A. I. Galochkin, “On estimates, unimprovable with respect to height, of some linear forms”, Mat. Sb. (N.S.), 124(166):3(7) (1984), 416–430; Math. USSR-Sb., 52:2 (1985), 407–421

Citation in format AMSBIB
\Bibitem{Gal84}
\by A.~I.~Galochkin
\paper On estimates, unimprovable with respect to height, of some linear forms
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 124(166)
\issue 3(7)
\pages 416--430
\mathnet{http://mi.mathnet.ru/msb2059}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=752228}
\zmath{https://zbmath.org/?q=an:0559.10028}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 52
\issue 2
\pages 407--421
\crossref{https://doi.org/10.1070/SM1985v052n02ABEH002897}


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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. Yu. V. Nesterenko, “Hermite–Padé approximants of generalized hypergeometric functions”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 189–219  mathnet  crossref  mathscinet  zmath  isi
    2. Ivankov P., “On Approximation of Values of Some Functions”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1994, no. 4, 12–15  mathscinet  zmath  isi
    3. Korobov A., “Multidimensional Chain Fractions and the Evaluation of Linear-Forms”, Acta Arith., 71:4 (1995), 331–349  crossref  mathscinet  zmath  isi
    4. P. L. Ivankov, “On the calculation of the constants involved in the estimation of linear forms”, Russian Math. (Iz. VUZ), 44:1 (2000), 29–35  mathnet  mathscinet  zmath  elib
    5. P. L. Ivankov, “O differentsirovanii po parametru”, Chebyshevskii sb., 16:3 (2015), 285–294  mathnet  elib
    6. P. L. Ivankov, “O differentsirovanii po parametru gipergeometricheskoi funktsii spetsialnogo vida”, Izv. vuzov. Matem., 2019, no. 12, 71–81  mathnet  crossref
    7. P. L. Ivankov, “O znacheniyakh gipergeometricheskoi funktsii s parametrom iz kvadratichnogo polya”, Chebyshevskii sb., 20:2 (2019), 178–185  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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