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Algebraic independence of some values of the exponential function. (English. Russian original) Zbl 0295.10027

Math. Notes 15, 391-398 (1974); translation from Mat. Zametki 15, 661-672 (1974).

MSC:

11J81 Transcendence (general theory)
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
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References:

[1] A. O. Gel’fond, Transcendental and Algebraic Numbers, Dover, New York (1960).
[2] M. Waldschmidt, ?Independance algebrique des valeurs de la fonction exponentielle,? Bull. Soc. Math. France,99, No. 4, 285-304 (1971). · Zbl 0224.10033
[3] A. A. Shmelev, ?On the problem of algebraic independence of algebraic powers of algebraic numbers,? Matem. Zametki,11, No. 6, 635-644 (1972). · Zbl 0254.10029
[4] A. O. Gel’fond, ?On algebraic independence of transcendental numbers of certain classes,? Usp. Matem. Nauk,4, No. 5, 14-48 (1949).
[5] A. O. Gel’fond and N. I. Fel’dman, ?On a measure of the relative transcendence of certain numbers,? Izv. Akad. Nauk SSSR, Ser. Matem.,14, 493-500 (1950).
[6] T. Shorey, ?On a theorem of Ramachandra,? Acta Arithm.,20, 215-221 (1972). · Zbl 0212.07203
[7] S. Lang, Introduction to Transcendental Numbers, Addison-Wesley, Reading, Mass. (1966). · Zbl 0144.04101
[8] N. I. Fel’dman, ?Refinement of an estimate for a linear form in the logarithms of algebraic numbers,? Matem. Sb., Novaya Ser.,77, No. 3, 423-436 (1968).
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