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A NOTE ON LACUNARY POWER SERIES WITH RATIONAL COEFFICIENTS
Published online by Cambridge University Press: 11 November 2015
Abstract
In this note, we prove that for any ${\it\nu}>0$, there is no lacunary entire function $f(z)\in \mathbb{Q}[[z]]$ such that $f(\mathbb{Q})\subseteq \mathbb{Q}$ and $\text{den}f(p/q)\ll q^{{\it\nu}}$, for all sufficiently large $q$.
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- Research Article
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- © 2015 Australian Mathematical Publishing Association Inc.
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