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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 2, Pages 253–284 (Mi izv1801)  

This article is cited in 17 scientific papers (total in 17 papers)

Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers

Yu. V. Nesterenko


Abstract: By the use of estimates for the multiplicities of the zeros of polynomials in certain fixed functions, an estimate is proved for the measure of algebraic independence of the values of the functions which is effective in the degree and height.
Bibliography: 10 titles.

Full text: PDF file (2790 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:2, 239–270

Bibliographic databases:

UDC: 517.9
MSC: Primary 10F35, 12D10; Secondary 33A35, 34A30, 34A20
Received: 30.12.1975

Citation: Yu. V. Nesterenko, “Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 41:2 (1977), 253–284; Math. USSR-Izv., 11:2 (1977), 239–270

Citation in format AMSBIB
\Bibitem{Nes77}
\by Yu.~V.~Nesterenko
\paper Estimates for the orders of zeros of functions of a~certain class and applications in the theory of transcendental numbers
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 2
\pages 253--284
\mathnet{http://mi.mathnet.ru/izv1801}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=491535}
\zmath{https://zbmath.org/?q=an:0354.10026|0378.10022}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 2
\pages 239--270
\crossref{https://doi.org/10.1070/IM1977v011n02ABEH001710}


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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. B. Shidlovskii, “On estimates for polynomials in values of $E$-functions”, Math. USSR-Sb., 43:1 (1982), 1–32  mathnet  crossref  mathscinet  zmath
    2. Charles F Osgood, “Nearly perfect systems and effective generalizations of Shidlovski's Theorem”, Journal of Number Theory, 13:4 (1981), 515  crossref
    3. 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
    4. Yu. V. Nesterenko, “On diophantine approximations in a field of $p$-adic numbers”, Russian Math. Surveys, 39:1 (1984), 173–174  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Yu. V. Nesterenko, “Estimates for the characteristic function of a prime ideal”, Math. USSR-Sb., 51:1 (1985), 9–32  mathnet  crossref  mathscinet  zmath  isi
    6. Yu. V. Nesterenko, “On algebraic independence of algebraic powers of algebraic numbers”, Math. USSR-Sb., 51:2 (1985), 429–454  mathnet  crossref  mathscinet  zmath  isi
    7. Yu. V. Nesterenko, “On a measure of the algebraic independence of the values of certain functions”, Math. USSR-Sb., 56:2 (1987), 545–567  mathnet  crossref  mathscinet  zmath  isi
    8. Yu. V. Nesterenko, “On the measure of algebraic independence of the values of an elliptic function at algebraic points”, Russian Math. Surveys, 40:4 (1985), 237–238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. Patrice Philippon, “Critères Pour L’indépendance Algébrique”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 64:1 (1986), 5  crossref  mathscinet  zmath
    10. W. V. Zudilin, “On rational approximations of values of a certain class of entire functions”, Sb. Math., 186:4 (1995), 555–590  mathnet  crossref  mathscinet  zmath  isi
    11. Yu. V. Nesterenko, “Modular functions and transcendence questions”, Sb. Math., 187:9 (1996), 1319–1348  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Teresa de Diego, “Points rationnels sur les familles de courbes de genre au moins 2”, Journal of Number Theory, 67:1 (1997), 85  crossref
    13. 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
    14. Susana Puddu, Juan Sabia, “An effective algorithm for quantifier elimination over algebraically closed fields using straight line programs”, Journal of Pure and Applied Algebra, 129:2 (1998), 173  crossref
    15. 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
    16. A. P. Dolgalev, “Estimates for the Orders of Zeros of Polynomials in Some Analytic Functions”, Math. Notes, 84:2 (2008), 184–196  mathnet  crossref  crossref  mathscinet  isi  elib
    17. E. Bombieri, D. Masser, U. Zannier, “Anomalous Subvarieties–Structure Theorems and Applications”, Internat Math Res Notices, 2010  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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