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Transcendence measures of exponentials and logarithms of algebraic numbers. (English) Zbl 0284.10013

MSC:
11J81 Transcendence (general theory)
11J04 Homogeneous approximation to one number
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References:
[1] P. Bundschuh : Zu einem Transzendenzsatz der Herren Baron und Braune , To appear in J. f.d. reine und angew. Math. · Zbl 0266.10028 · doi:10.1515/crll.1973.262-263.183 · crelle:GDZPPN002188295 · eudml:151357
[2] P.L. Cijsouw : Transcendence measures . (Thesis) University of Amsterdam, 1972. · Zbl 0252.10031
[3] N.I. Fel’Dman : Approximation of certain transcendental numbers. I. The approximation of logarithms of algebraic numbers . (Russian) Izv. Akad. Nauk SSSR, ser. mat., 15 (1951) 53-74.English translation: Amer. Math. Soc. Transl., II ser., 59 (1966) 224-245. · Zbl 0199.09605 · doi:10.1090/trans2/059/12
[4] N.I. Fel’Dman : Approximation of the logarithms of algebraic numbers by algebraic numbers . (Russian) Izv. Akad. Nauk SSSR, ser. mat., 24 (1960) 475-492.English translation: Amer. Math. Soc. Transl., II ser., 58 (1966) 125-142. · Zbl 0199.09602 · doi:10.1090/trans2/058/08
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[7] A.I. Galočkin : On the diophantine approximation of values of the exponential function and of solutions of certain transcendental equations. (Russian) Vestnik Moskov. Univ., Ser. I, 27 (3) (1972) 16-23. · Zbl 0259.10035 · eudml:125156
[8] A.O. Gel’Fond : Transcendental and algebraic numbers . (translated from the first Russian edition) Dover Publ., New York 1960. · Zbl 0090.26103
[9] F. Lindemann , Ueber die Zahl \pi . Math. Ann. 20 (1882) 213-225. · JFM 14.0369.04
[10] K. Mahler : An application of Jensen’s formula to polynomials . Mathematika 7 (1960) 98-100. · Zbl 0099.25003 · doi:10.1112/S0025579300001637
[11] T. Schneider : Einführung in die Transzendenten Zahlen . Springer Verlag, Berlin 1957. · Zbl 0077.04703
[12] R. Tijdeman : On the algebraic independence of certain numbers . Nederl. Akad. Wet. Proc., ser A, 74 (1971) 146-162= Indag. Math. 33 (1971) 146-162. · Zbl 0212.07103
[13] R. Tijdeman : An auxiliary result in the theory of transcendental numbers . J. Number Th. 5 (1973) 80-94. · Zbl 0254.10027 · doi:10.1016/0022-314X(73)90060-7
[14] M. Waldschmidt : Un premier cours sur les nombres transcendants . To appear in the Lecture Notes in Mathematics, Springer Verlag, Berlin. · Zbl 0302.10030
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