2014•arXiv (Cornell University)Open access
On transcendental analytic functions mapping an uncountable class of\n $U$-numbers into Liouville numbers
Diego Marques, Josimar Ramirez
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Abstract
In this paper, we shall prove, for any $m\\geq 1$, the existence of an\nuncountable subset of $U$-numbers of type $\\leq m$ (which we called the set of\n{\\it $m$-ultra numbers}) for which there exists uncountably many transcendental\nanalytic functions mapping it into Liouville numbers.\n
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