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Mat. Zametki, 1970, Volume 7, Issue 5, Pages 569–580 (Mi mz9541)  

This article is cited in 2 scientific papers (total in 3 papers)

An estimate of an incomplete linear form in several algebraic numbers

N. I. Fel'dman

M. V. Lomonosov Moscow State University

Abstract: Let $\mu>m-1$, let $\nu$ be a rational number, and let $\omega_k=b_k^\nu$, where $b_k\ne0$ are distinct numbers of an imaginary quadratic field $K$, which satisfy some additional conditions. Then
\begin{gather*} |x_1\omega_1+…+x_m\omega_m|>X^{-\mu},
X=\max_{1\leqslant k\leqslant m}|x_k|\geqslant X_0>0,
\end{gather*}
where $x_1,…,x_m$ are integers of the field $K$, and $X_0$ is an effective constant.

Full text: PDF file (1037 kB)

English version:
Mathematical Notes, 1970, 7:5, 343–349

Bibliographic databases:

UDC: 511
Received: 12.05.1969

Citation: N. I. Fel'dman, “An estimate of an incomplete linear form in several algebraic numbers”, Mat. Zametki, 7:5 (1970), 569–580; Math. Notes, 7:5 (1970), 343–349

Citation in format AMSBIB
\Bibitem{Fel70}
\by N.~I.~Fel'dman
\paper An estimate of an incomplete linear form in several algebraic numbers
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 5
\pages 569--580
\mathnet{http://mi.mathnet.ru/mz9541}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=268127}
\zmath{https://zbmath.org/?q=an:0212.39402}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 5
\pages 343--349
\crossref{https://doi.org/10.1007/BF01123845}


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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, “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
    2. V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. N. M. Korobov, Yu. V. Nesterenko, A. B. Shidlovskii, “Naum Il'ich Feld'man (obituary)”, Russian Math. Surveys, 50:6 (1995), 1247–1252  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математические заметки Mathematical Notes
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