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References
W.D. Brownawell, The algebraic independence of certain values of the exponential function, K. norske Vidensk. Selsk. Skr., No. 23 (1972), 5p.
—, Sequences of diophantine approximations, J. Number Th. 6 (1974), 11–21.
—, The algebraic independence of certain numbers related by the exponential function, J. Number Th. 6 (1974), 22–31.
—, Gelfond's method for algebraic independence, Trans. A.M.S. 210 (1975), 1–26.
—, Pairs of polynomials small at a number to certain algebraic powers, Sem. Delange Pisot Poitou, 17e année (1975/76), No. 11
—, Some remarks on semi-resultants, Chapter 14 in Transcendence Theory: Advances and Applications, A. Baker and D.W. Masser, eds, Academic Press, London, 1977.
—, On the Gelfond-Feldman measure of algebraic independence, Compositio Math. (to appear)
W.D. Brownawell and M. Waldschmidt, The algebraic independence of certain numbers to algebraic powers, Acta Arith. 32 (1977), 63–71.
J.W.S. Cassels, An Introduction to Diophantine Approximations, Cambridge University Press, Cambridge, 1957.
G.V. Chudnovsky, The algebraic independence of certain values of the exponential function, Mat. Zametki 15 (1974), 661–672; Math. Notes 15 (1974), 391–398.
—, Some analytic methods in the theory of transcendental numbers, Ukrainian SSR Academy of Sciences, Preprint IM-74-8, Kiev, 1974, 48 p.; Analytic methods in diophantine approximations, id., IM-74-9, Kiev, 1974, 52 p.
—, A mutual transcendence measure for some classes of numbers, Dokl. Akad. Nauk SSSR 218 (1974), 771–774; Soviet Math. Dokl. 15 (1974), 1424–1428.
—, Towards the Schanuel hypothesis; algebraic curves near a point. Part I. General theory of colored sequences, 33p. Part II. Fields of finite type of transcendence and colored sequences; resultants, 23 p. (manuscript)
G.V. Chudnovsky, Algebraic grounds for the proof of algebraic independence. How to obtain a measure of algebraic independence using elementary methods, Part I. Elementary algebra, 30 p. (manuscript)
—, Explicit construction of auxiliary functions for transcendental numbers, these Proceedings.
P.L. Cijsouw, Transcendence Measures, Thesis, Amsterdam, 1972.
A.O. Gelfond, Transcendental and Algebraic Numbers, GITTL, Moscow, 1952; Dover, New York, 1960.
A.O. Gelfond and N.I. Feldman, On the measure of relative transcendence of certain numbers, Izv. Akad. Nauk SSSR 14 (1950), 493–500.
S. Lang, Introduction to Transcendental Numbers, Addison-Wesley, Reading, Mass., 1966.
M. Mignotte and M. Waldschmidt, Linear forms in logarithms and Schneider's method, Math. Ann. 231 (1978), 241–267.
Th. Schneider, Einführung in die transzendenten Zahlen, Springer, Berlin, 1957.
A.A. Smelev, On the method of A.O. Gelfond in the theory of transcendental numbers, Mat. Zametki 10 (1971), 415–426; Math Notes 10 (1971), 672–678.
R. Tijdeman, On the number of zeros of general exponential polynomials, Nederl. Akad. Wetensch. Proc. Ser. A 74 = Indag. Math. 33 (1971), 1–7.
—, On the algebraic independence of certain numbers, Nederl. Akad. Wetensch. Proc. Ser. A 74 = Indag. Math. 33 (1971), 146–162.
—, An auxiliary result in the theory of transcendental numbers, J. Number Th. 5 (1973), 80–94.
M. Waldschmidt, Solution d'un problème de Schneider sur les nombres transcendants, C.R. Acad. Sci. Ser. A-B. 271 (1970), A697–700.
—, Indépendance algébrique des valeurs de la fonction exponentielle, Bulletin Soc. Math. France 99 (1971), 285–304.
—, Solution du huitième probleme de Schneider, J. Number Th. 5 (1973), 191–202.
—, Indépendance algébrique par la methode de G.V. Chudnovsky, Sem. Delange Pisot Poitou, 16e annee (1974/75), No. G8, 18 p
M. Waldschmidt, Les travaux de G.V. Chudnovsky sur les nombres transcendants, Sem. Bourbaki, 28e annee, 1975/76, No. 488, 15 p.
R. Wallisser, reported in Review 10021, Zbl. Math. 241 (1973), 45–46 by P. Bundschuh.
P. Warkentin, Algebraische Unabhängigkeit gewisser p-adischer Zahlen, Diplomarbeit, Freiburg, 1978.
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Brownawell, W.D. (1979). On the development of Gelfond's method. In: Nathanson, M.B. (eds) Number Theory Carbondale 1979. Lecture Notes in Mathematics, vol 751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062700
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