On transcendental analytic functions mapping an uncountable class of \(U\)-numbers into Liouville numbers. (English) Zbl 1311.11067

Summary: In this paper, we shall prove, for any \(m\geq 1\), the existence of an uncountable subset of \(U\)-numbers of type \(\leq m\) (which we called the set of \(m\)-ultra numbers) for which there exists uncountably many transcendental analytic functions mapping it into Liouville numbers.


11J81 Transcendence (general theory)
11J89 Transcendence theory of elliptic and abelian functions
11J91 Transcendence theory of other special functions
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