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Linear forms and simultaneous approximations. (English) Zbl 0345.10021


MSC:

11J81 Transcendence (general theory)
11J17 Approximation by numbers from a fixed field
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References:

[1] A. Baker : A sharpening of the bounds for linear forms in logarithms . Acta Arith. 21 (1972) 117-129. · Zbl 0244.10031
[2] A. Baker : A central theorem in transcendence theory . In Diophantine approximation and its applications , ed. by C. F. Osgood (Academic Press, 1973), 1-23. · Zbl 0262.10022
[3] A. Baker : A sharpening of the bounds for linear forms in logarithms III . Acta Arith. 27 (1975) 247-252. · Zbl 0301.10030
[4] A. Baker and H.M. Stark : On a fundamental inequality in number theory . Annals of Math. 94 (1971) 190-199. · Zbl 0219.12009
[5] P. Bundschuh : Zum Franklin-Schneiderschen Satz . J. reine und angew. Math. 260 (1973) 103-118. · Zbl 0256.10020
[6] P. Bundschuh : Zur Simultanen Approximation von \beta 0, ..., \beta n-1, und \Pi n-1v=0 \alpha \beta vv durch algebraische Zahlen . J. reine und angew. Math. 278-279 (1975) 99-117. · Zbl 0311.10034
[7] P.L. Cijsouw : Transcendence measures of certain numbers whose transcendency was proved by A. Baker . Compositio Math. 28 (1974) 179-194. · Zbl 0284.10014
[8] P. Franklin : A new class of transcendental numbers . Trans. Amer. Math. Soc. 42 (1937) 155-182. · Zbl 0017.15205
[9] F. Meyer : Transcendence of exponential products with ”nearly algebraic” exponents (to appear) .
[10] G. Ricci : Sul settimo problema di Hilbert . Ann. Pisa (2) 4 (1935) 341-372. · Zbl 0012.24801
[11] Th. Schneider : Einführung in die transzendenten Zahlen . Berlin-Göttingen-Heidelberg, Springer-Verlag, 1957. · Zbl 0077.04703
[12] A.A. Smelev : A. O. Gelfond’s method in the theory of transcendental numbers . Mat. Zam. 10 (1971) 415-426 (English translation: Math. Notes 10 (1971) 672-678). · Zbl 0254.10028
[13] R. Tijdeman : On the equation of Catalan . Acta Arith. 29 (1976) 197-209. · Zbl 0286.10013
[14] M. Waldschmidt : Nombres transcendants . Lecture notes in Math. 402, Springer-Verlag, 1974. · Zbl 0302.10030
[15] R. Wallisser : Über Produkte transzendenter Zahlen . J. reine und angew. Math. 258 (1973) 62-78. · Zbl 0257.10014
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