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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 4, Pages 723–751 (Mi izv1861)  

This article is cited in 1 scientific paper (total in 1 paper)

The Thue–Mahler equation in a relative field and approximation of algebraic numbers by algebraic numbers

S. V. Kotov, V. G. Sprindzhuk


Abstract: A new estimate of the solutions of the generalized Thue–Mahler equation is derived, which explicitly exhibits the influence of all fundamental parameters of the equation on the magnitude of the solutions. Also, an effective power sharpening is given of “Liouville's inequality” relating to the approximation of algebraic numbers by algebraic numbers of a fixed field, which includes both Archimedean and non-Archimedean valuations.
Bibliography: 19 titles.

Full text: PDF file (2266 kB)
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English version:
Izvestiya: Mathematics, 1977, 41:4, 677–707

Bibliographic databases:

UDC: 511
MSC: 10B05, 10B45, 10F25, 10F30
Received: 16.01.1976

Citation: S. V. Kotov, V. G. Sprindzhuk, “The Thue–Mahler equation in a relative field and approximation of algebraic numbers by algebraic numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 41:4 (1977), 723–751; Izv. Math., 41:4 (1977), 677–707

Citation in format AMSBIB
\Bibitem{KotSpr77}
\by S.~V.~Kotov, V.~G.~Sprindzhuk
\paper The Thue--Mahler equation in a~relative field and approximation of algebraic numbers by algebraic numbers
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 4
\pages 723--751
\mathnet{http://mi.mathnet.ru/izv1861}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=485717}
\zmath{https://zbmath.org/?q=an:0358.10008}
\transl
\jour Izv. Math.
\yr 1977
\vol 41
\issue 4
\pages 677--707
\crossref{https://doi.org/10.1070/IM1977v011n04ABEH001741}


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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. V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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