This is a preview of subscription content, log in via an institution to check access.
References
A. O. Gel'fond, “On the algebraic independence of transcendental numbers of some classes,”Usp. Mat. Nauk,4, No. 5, 14–48 (1949).
A. O. Gel'fond,Transcendental and Algebraic Numbers [in Russian], Gostekhizdat, Moscow (1952).
A. A. Shmelev, “Simultaneous approximation of exponents by elements of fields whose transcendency power is equal to unity,”Mat. Zametki,48, No. 6, 126–136 (1990).
A. A. Shmelev, “On the question of algebraic independence of exponents,”Mat. Zametki,17, No. 3, 407–418 (1975).
A. A. Shmelev, “Simultaneous approximation of exponents by polynomials in a given transcendental number,”Ukr. Mat. Zh.,27, No. 4, 555–563 (1975).
R. Tijdeman, “An auxiliary result in the theory of transcendental numbers,”J. Number Theory, No. 5, 191–202 (1973).
G. V. Chudnovskii, “Algebraic independence of several values of an exponential function,”Mat. Zametki,15, No. 4, 661–672 (1974).
N. I. Fel'dman,Seventh Hilert Problem [in Russian], Izdat. Mosk. Univ., Moscow (1982).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 56, No. 1, pp. 122–134, July, 1994.
Rights and permissions
About this article
Cite this article
Shmelev, A.A. On a simultaneous approximation of logarithms and algebraic powers of algebraic numbers. Math Notes 56, 734–744 (1994). https://doi.org/10.1007/BF02110565
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02110565