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Transcendence degree of some fields generated by values of the exponential function. (English. Russian original) Zbl 0704.11015

Math. Notes 46, No. 3, 706-712 (1989); translation from Mat. Zametki 46, No. 3, 40-49 (1989).
See the review in Zbl 0691.10030.

MSC:

11J85 Algebraic independence; Gel’fond’s method
11J81 Transcendence (general theory)
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References:

[1] A. O. Gel’fond, ?On the algebraic independence of algebraic powers of algebraic numbers,? Dokl. Akad. Nauk SSSR,64, No. 3, 277-280 (1949). · Zbl 0039.04303
[2] A. O. Gel’fond, ?On the algebraic independence of transcendental numbers of certain classes,? Usp. Mat. Nauk,4, No. 5, 14-48 (1949).
[3] O. Zariski and P. Samuel, Commutative Algebra, Vol. 2, van Nostrand, Princeton, N. J. (1960). · Zbl 0121.27801
[4] Yu. V. Nesterenko, ?On a sufficient criterion for the algebraic independence of numbers,? Vestn. Mosk. Gos. Univ. Ser. 1, Mat. Mekh., No. 4, 63-68 (1983).
[5] Yu. V. Nesterenko, ?On the algebraic independence of algebraic powers of algebraic numbers,? Mat. Sb.,123 (165), No. 4, 435-459 (1984). · Zbl 0549.10023
[6] Yu. V. Nesterenko, ?A measure of the algebraic independence of values of certain functions,? Mat. Sb.,128 (170). No. 12, 545-568 (1985). · Zbl 0603.10033
[7] G. Dias, ?Grands degrés de transcendance pour des familles d’exponentielles,? C. R. Acad. Sci. Paris,305, Sér. I, No. 5, 159-162 (1987).
[8] Yu. V. Nesterenko, ?On the algebraical independence of algebraic numbers to algebraic powers,? C. R. Conference ?Approximations Diophantiennes et Nombres Transcendants,? Luminy, 1982. Progress in Math.,31, 199-220 (1983).
[9] P. Philippen, ?Critères pour l’indépendance algébrique,? Publ. Math. IHES, No. 64, 5-52 (1986).
[10] R. Tijdeman, ?An auxiliary result in the theory of transcendental numbers,? J. Number Theory,5, 80-94 (1973). · Zbl 0254.10027 · doi:10.1016/0022-314X(73)90060-7
[11] M. Waldschmidt, Nombres Transcendants, Lecture Notes in Mathematics, Vol. 402, Springer, Berlin (1974).
[12] M. Waldschmidt, ?Algebraic independence of transcendental numbers. Gel’fond’s method and its developments,? in: Anniversary of Oberwolfach, Perspectives in Mathematics, Birkhäuser (1984), pp. 551-571. · Zbl 0556.10023
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