Geodesic
Algebraic independence of some values of the exponential function
Matematičeskie zametki, Tome 15 (1974) no. 4, pp. 661-672 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove general results concerning the algebraic independence of three values of the exponential function. For $\beta$ algebraic and of degree 7 and $\alpha$ algebraic and $\neq0,\,1$ there exist among the numbers $\alpha^\beta,\dots,\alpha^{\beta^6}$ three which are algebraically independent. The proof employs a method due to A. O. Gel'fond and N. I. Fel'dman. 
@article{MZM_1974_15_4_a17,
     author = {G. V. Chudnovskii},
     title = {Algebraic independence of some values of the exponential function},
     journal = {Matemati\v{c}eskie zametki},
     pages = {661--672},
     year = {1974},
     volume = {15},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_4_a17/}
}
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G. V. Chudnovskii. Algebraic independence of some values of the exponential function. Matematičeskie zametki, Tome 15 (1974) no. 4, pp. 661-672. http://geodesic.mathdoc.fr/item/MZM_1974_15_4_a17/