Abstract
Given the three numbers of,a 1β 2β , and Ina 2/Ina 1, wherea 1 anda 2 are algebraic numbers whose logarithms are linearly independent in a rational field andΒ is a quadratic irrationality, it is shown that they are not all expressible algebraically in terms of one of them.
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Literature cited
A. O. Gel'fond, “Sur le septieme probleme de Hubert,” Izv. Akad. Nauk SSSR, ser. fiz.-matem.,4, 623–630 (1934).
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Additional information
Translated from Matematicheskie Zametki, Vol.3, No. 1, pp. 51–58, January, 1968.
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Shmelev, A.A. Concerning algebraic independence of some transcendental numbers. Mathematical Notes of the Academy of Sciences of the USSR 3, 31–35 (1968). https://doi.org/10.1007/BF01386962
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DOI: https://doi.org/10.1007/BF01386962