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ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER
Published online by Cambridge University Press: 12 May 2016
Abstract
In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].
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- © 2016 Australian Mathematical Publishing Association Inc.
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