Literature cited
M. Waldschmidt, “Solution d'un problème de Schneider sur les nombres transcendants,” C. R. Acad. Sci.,271, No. 15, A679-A700 (1970).
M. Waldschmidt, “Solution du huitième problème de Schneider,” J. Number Theory,5, No. 3, 191–202 (1973).
D. W. Brownawell, “The algebraic independence of certain numbers related by the exponential function,” J. Number Theory,6, No. 1, 22–31 (1974).
A. O. Gel'fond, “On the algebraic independence of transcendental numbers of certain classes,” Usp. Mat. Nauk,4, No. 5, 14–48 (1949).
A. O. Gel'fond, Transcendental and Algebraic Numbers [in Russian], Gostekhizdat, Moscow (1952).
A. B. Shidlovskii, Diophantine Approximations and Transcendental Numbers [in Russian], Moscow State Univ., Moscow (1982).
A. A. Shmelev, “On a question concerning algebraic independence of exponents,” Mat. Zametki,17, No. 3, 407–418 (1975).
A. A. Shmelev, “Combined approximations of exponents by means of elements of field Q1,” Mat. Zametki,30, No. 1, 3–12 (1981).
A. A. Shmelev, “Combined approximations of exponents by means of polynomials in a given transcendental number,” Ukr. Mat. Zh.,27, No. 4, 555–563 (1975).
A. O. Gel'fond and N. I. Fel'dman, “On a measure of the mutual transcendance of certain numbers,” Izv. Akad. Nauk SSSR, Ser. Mat.,14, No. 5, 493–500 (1950).
R. Bellman, Introduction to the Theory of Matrices [Russian translation], Nauka, Moscow(1969).
O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, D. Van Nostrand, Princeton (1958).
E. Hecke, Lectures on the Theory of Algebraic Numbers [Russian translation from German], GTTI, Moscow (1940).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 48, No. 5, pp. 128–137, November, 1990.
Rights and permissions
About this article
Cite this article
Shmelev, A.A. Combined approximations of some transcendental numbers. Mathematical Notes of the Academy of Sciences of the USSR 48, 1163–1170 (1990). https://doi.org/10.1007/BF01236305
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01236305