On transcendental analytic functions mapping an uncountable class of U-numbers into Liouville numbers
Abstract
In this paper, we shall prove, for any m≥ 1, the existence of an uncountable subset of U-numbers of type ≤ m (which we called the set of m-ultra numbers) for which there exists uncountably many transcendental analytic functions mapping it into Liouville numbers.
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