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ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  12 May 2016

DIEGO MARQUES  and
JOSIMAR RAMIREZ
DIEGO MARQUES*
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brasília, 70910-900, Brazil email [email protected]
JOSIMAR RAMIREZ
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brasília, 70910-900, Brazil email [email protected]
*
✉[email protected]
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Abstract

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In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].

Keywords

exceptional settranscendental function

MSC classification

Primary: 11J81: Transcendence (general theory)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 15 - 19
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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Mahler, K., Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976).CrossRefGoogle Scholar
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