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An elementary existence theorem for entire functions

Published online by Cambridge University Press:  17 April 2009

Kurt Mahler
Kurt Mahler
Affiliation:
Department of Mathematics, Ohio State University, Columbus, Ohio, USA.
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Abstract

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It is proved that, for any m given distinct real numbers a1, …, am, there exist transcendental entire functions f(z) at most of order m for which all the values

are rational integers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 415 - 419
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Mahler, Kurt, “An arithmetic remark on entire periodic functions”, Bull. Austral. Math. Soc. 5 (1971), 191–195.CrossRefGoogle Scholar