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ON A VARIANT OF A QUESTION PROPOSED BY K. MAHLER CONCERNING LIOUVILLE NUMBERS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 July 2014

DIEGO MARQUES  and
CARLOS GUSTAVO MOREIRA
DIEGO MARQUES*
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brasília, DF, Brazil email diego@mat.unb.br
CARLOS GUSTAVO MOREIRA
Affiliation:
Instituto de Matemática Pura e Aplicada, Rio de Janeiro, RJ, Brazil email gugu@impa.br
*
✉dyhegu2@gmail.com
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Abstract

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In this note we shall prove the existence of an uncountable subset of Liouville numbers (which we call the set of ultra-Liouville numbers) for which there exist uncountably many transcendental analytic functions mapping the subset into itself.

Keywords

Liouville numbersultra-Liouville numberstranscendental function

MSC classification

Primary: 11J04: Homogeneous approximation to one number
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 29 - 33
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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