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Degree-free bounds for dependence relations

Published online by Cambridge University Press:  09 April 2009

A. Bijlsma  and
P. L. Cijsouw
A. Bijlsma
Affiliation:
Eindhoven Technological University, Department of Mathematics, P. O. Box 513, 5600 MB Eindhoven, Netherlands
P. L. Cijsouw
Affiliation:
Eindhoven Technological University, Department of Mathematics, P. O. Box 513, 5600 MB Eindhoven, Netherlands
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Abstract

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Let α1,…, αn be non-zero albegraic numbers and let l1(α1),…ln(αn) denote arbitrary fixed values of the logarithms of α1,…n, respectively Given that l1(α1),…ln(αn) are linearly dependent over Q, the existence of non-trival dependence relation between these numbers with integer coefficients of low absolute values can be proved. Existing results of this kind give bounds for the absolute values of the coefficients which are expressions in the degree D = [Q(α1…αn): Q], the heights of α1,…αn and the magnitudes of the logarithms involved.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 496 - 507
Copyright
Copyright © Australian Mathematical Society 1981

References

Baker, A. (1975), ‘A sharpening of the bounds for linear forms in logarithms (III)’. Acta Arith. 27, 247–252.CrossRefGoogle Scholar
Bijlsma, A. (1978), Simultaneous approximations in transcendental number theory. Mathematical Centre Tracts 94 (Mathematisch Centrum, Amsterdam).Google Scholar
Cijsouw, P. L. (1974), ‘Transcendence measures of exponentials and logarithms of algebraic numbers’. Compositio Math. 28, 163–178.Google Scholar
Mignotte, M. and Waldschmidt, M. (1977), ‘Approximation simultanée de valeurs de la fonction exponentielle’. Compositio Math. 34, 127–139.Google Scholar
van der Poorten, A. J. and Loxton, J. H. (1977), ‘Multiplicative relations in number fields’. Bull. Austral. Math. Soc. 16, 83–98.CrossRefGoogle Scholar
Schinzel, A. (1978), ‘Reducibility of lacunary polynomials, III’. Acta Arith. 34, 227–266.CrossRefGoogle Scholar
Schneider, Th. (1957), Einführung in die transzendenten Zahlen. (Springer Verlag, Berlin).CrossRefGoogle Scholar
Tijdeman, R. (1971), ‘On the number of zeros of general exponential polynomials’. Nederl. Akad. Wetensch. Proc. Ser. A 74 = Indag. Math. 33, 1–7.Google Scholar
Waldschmidt, M. (1980), ‘A lower bound for linear forms in logarithms’. Acta Arith. 37, 257–283.Google Scholar