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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 4(12), Pages 545–568 (Mi msb2175)  

This article is cited in 14 scientific papers (total in 14 papers)

On a measure of the algebraic independence of the values of certain functions

Yu. V. Nesterenko


Abstract: Estimates are established for a measure of the algebraic independence of the values of the exponential function and certain other functions, and a theorem is proved on the number of algebraically independent quantities among a series of values of the exponential function.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:2, 545–567

Bibliographic databases:

UDC: 511.36
MSC: Primary 11J82; Secondary 11J85, 11J91
Received: 28.01.1985

Citation: Yu. V. Nesterenko, “On a measure of the algebraic independence of the values of certain functions”, Mat. Sb. (N.S.), 128(170):4(12) (1985), 545–568; Math. USSR-Sb., 56:2 (1987), 545–567

Citation in format AMSBIB
\Bibitem{Nes85}
\by Yu.~V.~Nesterenko
\paper On a~measure of the algebraic independence of the values of certain functions
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 4(12)
\pages 545--568
\mathnet{http://mi.mathnet.ru/msb2175}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=820402}
\zmath{https://zbmath.org/?q=an:0608.10034|0603.10033}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 2
\pages 545--567
\crossref{https://doi.org/10.1070/SM1987v056n02ABEH003051}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985G744500016}


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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. Brownawell W., “Large Transcendence Degree Revisited .1. Exponential and Non-Cm Cases”, Lect. Notes Math., 1290 (1987), 149–173  crossref  mathscinet  zmath  isi
    2. Guy Diaz, “Grands degrés de transcendance pour des familles d'exponentielles”, Journal of Number Theory, 31:1 (1989), 1  crossref
    3. Nesterenko Y., “Estimates of the Number of Null Functions of Certain Classes”, Acta Arith., 53:1 (1989), 29–46  mathscinet  zmath  isi
    4. Brownawell W., “Applications of Cayley-Chow Forms”, Lect. Notes Math., 1380 (1989), 1–78  crossref  mathscinet  isi
    5. Shestakov S., “Transcendence Degree of Certain Fields Generated by Values of Elliptic Functions”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1991, no. 3, 30–36  mathscinet  isi
    6. Shestakov S., “On Some Numbers Algebraic Independence Measure”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1992, no. 2, 8–12  mathscinet  isi
    7. Amoroso F., “Values of Polynomials with Integer Coefficients and Distance to their Common Zeros”, Acta Arith., 68:2 (1994), 101–112  mathscinet  zmath  isi
    8. Yu. V. Nesterenko, “On a measure of algebraic independence of values of an elliptic function”, Izv. Math., 59:4 (1995), 815–838  mathnet  crossref  mathscinet  zmath  isi
    9. M. Giusti, J. Heintz, K. Hägele, J.E. Morais, L.M. Pardo, J.L. Montaña, “Lower bounds for diophantine approximations”, Journal of Pure and Applied Algebra, 117-118 (1997), 277  crossref
    10. Ya. M. Kholyavka, “On a measure of algebraic independence of values of Jacobi elliptic functions”, J. Math. Sci., 146:2 (2007), 5782–5790  mathnet  crossref  mathscinet  zmath  elib
    11. Yu. V. Nesterenko, “Algebraic independence of $p$-adic numbers”, Izv. Math., 72:3 (2008), 565–579  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. Bundschuh P., “Transcendence and Algebraic Independence of Series Related to Stern's Sequence”, Int. J. Number Theory, 8:2 (2012), 361–376  crossref  mathscinet  zmath  isi
    13. M. E. Zelenova, “Solving Polynomial Systems in Integers”, Math. Notes, 98:3 (2015), 399–413  mathnet  crossref  crossref  mathscinet  isi  elib
    14. Chirskii V.G., “Topical Problems of the Theory of Transcendental Numbers: Development of Approaches to Their Solution in the Works of Yu. V. Nesterenko”, Russ. J. Math. Phys., 24:2 (2017), 153–171  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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