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On the Taylor coefficients of rational functions

Published online by Cambridge University Press:  24 October 2008

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

Let F(z) be a rational function of z which is regular at z = 0 and so possesses a convergent power series

The problem arises of characterizing those rational functions F(z) that have infinitely many vanishing Taylor coefficients fh. After earlier and more special results by Siegel(2) and Ward(4) I applied in 1934(1) a p-adic method due to Skolem(3) to the problem and obtained the following partial solution.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 1 , January 1956 , pp. 39 - 48
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

REFERENCES

(1) Mahler, K. Proc. Acad. Sci. Amst. 38 (1935), 51–60.Google Scholar
(2) Siegel, C. L. Tôhoku math. J. 20 (1921), 26–31.Google Scholar
(3) Skolem, Th. Skr. norske Vidensk Akad. (1933), no. 6.Google Scholar
(4) Ward, M. Math. Z. 39 (1934), 211–14.Google Scholar