Proceedings of the Japan Academy, Series A, Mathematical Sciences

On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers

Diego Marques and Josimar Ramirez

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 2 (2015), 25-28.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1422885265

Digital Object Identifier
doi:10.3792/pjaa.91.25

Mathematical Reviews number (MathSciNet)
MR3310967

Zentralblatt MATH identifier
1311.11067

Subjects
Primary: 11Jxx: Diophantine approximation, transcendental number theory [See also 11K60]

Keywords
Transcendental functions $m$-ultra number Liouville height

Citation

Marques, Diego; Ramirez, Josimar. On transcendental analytic functions mapping an uncountable class of $U$-numbers into Liouville numbers. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 2, 25--28. doi:10.3792/pjaa.91.25. https://projecteuclid.org/euclid.pja/1422885265


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References

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