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A. O. Gel'fond's method in the theory of transcendental numbers

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Abstract

Obtained in this work, with the help of a method of A. O. Gel'fond, are several results on algebraic independence of the values of an exponential function at nonalgebraic points.

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Literature cited

  1. A. O. Gel'fond, “On algebraic independence of transcendental numbers of certain classes,” Uspekhi Matem. Nauk,4, No. 5 (33), 14–48 (1949).

    Google Scholar 

  2. A. O. Gel'fond, Transcendental and Algebraic Numbers [in Russian], Moscow (1952).

  3. P. Franklin, “A new class of transcendental numbers,” Trans. Amer. Math. Soc.,42, 155–182 (1937).

    Google Scholar 

  4. T. Schneider, Einfuhrüng in die transzendente Zahlen, Berlin, 1957.

  5. N. I. Fel'dman and A. B. Shidlovskii, “The development and present state of the theory of transcendental numbers,” Uspekhi Matem. Nauk,22, No. 3 (135), 3–81 (1967).

    Google Scholar 

  6. N. I. Fel'dman, “Arithmetic properties of the solutions of a transcendental equation,” Vestnik Moskv. Gos. Univ., Ser. I, No. 1, 13–20 (1964).

    Google Scholar 

  7. N. I. Fel'dman, “Approximation of some transcendental numbers, I” Izv. Akad. Nauk SSSR, Ser. Matem.,15, 53–74 (1951).

    Google Scholar 

  8. S. Lang, Introduction to Transcendental Numbers, London (1966).

  9. A. O. Gel'fond and Yu. V. Linnik, Elementary Methods in Analytic Number Theory [in Russian], Moscow (1962).

  10. N. I. Fel'dman, “Refinement of bounds of linear forms in logarithms of algebraic numbers,” Matem. Sbornik,77 (119), No. 3, 423–436 (1969).

    Google Scholar 

  11. N. I. Fel'dman, “On approximation by algebraic numbers of logarithms of algebraic numbers,” Izv. Akad. Nauk SSSR, Ser. Matem.,24, 475–492 (1960).

    Google Scholar 

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Authors and Affiliations

  1. Moscow Scientific Research-Institute of Instruments Construction, USSR

    A. A. Shmelev

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  1. A. A. Shmelev
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Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 415–426, October, 1971.

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Shmelev, A.A. A. O. Gel'fond's method in the theory of transcendental numbers. Mathematical Notes of the Academy of Sciences of the USSR 10, 672–678 (1971). https://doi.org/10.1007/BF01106463

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  • DOI: https://doi.org/10.1007/BF01106463

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