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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.

MSC:

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