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By Serge Lang, Hale Trotter

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Formules d'Her mite pour les approximants de Fade de logarithmes et de fonetions binomes, et mesures d''irrationalite, C. R. Acad. Sci. Paris Ser. A 288A (1979), A965-A967. C18. , Algebraic independence of constants connected with exponential and elliptic functions, Meeting of AMS, Pullman, Washington, June 1975, Notices Amer. Math. Soc. 22 (1975), A-486. C19. , This volume, Chapters 1, 4, 7, 8. C20. P. L. Cijsouw, Transcendence measures, Thesis, 1972. C21. J. Coates, Linear relations between liri and the periods of two elliptic curves, Diophantine Approximation and its Applications, Academic Press, London, 1973, pp.

40), we obtain that ANALYTIC METHODS 45 Q t m ( z ) is divisible by P(z). ,M — 1. However, we have assumed that r is the smallest power to which P(z) occurs in all Ckm(z). 7) for sufficiently large c0 > 0. The theorem is proved. 5. Suppose P(x) G Z[x], P(x) ^ 0, is a polynomial of degree < d and height < i/. 77ze« there exists an absolute constant c'0 > 0 ^wc/z //za/ |P(e)|>exp(-c^2ln(/ta)ln2d). 6. There exists an effectively computable constant c$ > 0 such that \e - £ | > exp(-c^/ 2 ln(ift/)ln 2 d) for all algebraic numbers £ of degree < d a«d height < //.

24 (1973), 251-259. 510. C. L. Stewart, On a theorem of Kronecker and related question of Lehmer, Seminaire de Theorie des Nombres (Bordeaux, 1977-78), No. 7, 11pp. 511. A. Selberg and S. D. Chowla, On Epstein's zeta-function, J. Reine Angew. Math. 227 (1967), 86-110. Tl. R. Tijdeman, On the number of zeroes of general exponential polynomials, Indag. Math. 33 (1971), 1-7. T2. , Exponential diophantine equations, Proc. Internat. Congr. Math. (Helsinki, 1978), vol. 1, Acad. Sci. , Helsinki, 1980, pp.

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