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February 2015 On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers
Diego Marques, Josimar Ramirez
Proc. Japan Acad. Ser. A Math. Sci. 91(2): 25-28 (February 2015). DOI: 10.3792/pjaa.91.25

Abstract

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 \textit{$m$-ultra numbers}) for which there exists uncountably many transcendental analytic functions mapping it into Liouville numbers.

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Diego Marques. Josimar Ramirez. "On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers." Proc. Japan Acad. Ser. A Math. Sci. 91 (2) 25 - 28, February 2015. https://doi.org/10.3792/pjaa.91.25

Information

Published: February 2015
First available in Project Euclid: 2 February 2015

zbMATH: 1311.11067
MathSciNet: MR3310967
Digital Object Identifier: 10.3792/pjaa.91.25

Subjects:
Primary: 11Jxx

Keywords: $m$-ultra number , Height , Liouville , transcendental functions

Rights: Copyright © 2015 The Japan Academy

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Vol.91 • No. 2 • February 2015
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