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An application of Jensen's formula to polynomials

Published online by Cambridge University Press:  26 February 2010

K. Mahler
K. Mahler
Affiliation:
Mathematics Department, Manchester University
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Extract

In this note new proofs will be given for two inequalities on polynomials due to N. I. Feldman [1] and A. 0. Gelfond [2], respectively; these inequalities are of importance in the theory of transcendental numbers. While the original proofs by the two authors are quite unconnected, we shall deduce both results from the same source, viz. from Jensen's integral formula in the theory of analytic functions.

Type
Research Article
Information
Mathematika , Volume 7 , Issue 2 , December 1960 , pp. 98 - 100
Copyright
Copyright © University College London 1960

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References

1.Feldman, N. I., “Approksimatsiya nekotorych transtsendentnych tchisel, I,” Izvestiya Akad. Nauk SSSR., ser. mat. 15 (1951), 53–74; Lemma 2, p. 54.Google Scholar
2.Gelfond, A. O., Transtsendentnye i algebraitcheskie tchisla (Moskva 1952), pp. 22–24 (Lemma 4) and pp. 168–173 (Lemma II).Google Scholar