## 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

### Keywords:

transcendental functions; $$m$$-ultra number; Liouville; height
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### References:

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