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ALGEBRAIC VALUES OF TRANSCENDENTAL FUNCTIONS AT ALGEBRAIC POINTS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  22 June 2010

JINGJING HUANG ,
DIEGO MARQUES  and
MARTIN MEREB
JINGJING HUANG
Affiliation:
Mathematics Department, Pennsylvania State University, PA 16802, USA (email: huang@math.psu.edu)
DIEGO MARQUES*
Affiliation:
Departamento De Matemática, Universidade de Brasília, Brasília, CEP: 70910–900 DF, Brazil (email: diego@mat.unb.br)
MARTIN MEREB
Affiliation:
Mathematics Department, University of Texas at Austin, TX 78712, USA (email: mmereb@gmail.com)
*
✉For correspondence; e-mail: diego@mat.unb.br
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Abstract

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It is shown that any subset of can be the exceptional set of some transcendental entire function. Furthermore, we give a much more general version of this theorem and present a unified proof.

Keywords

exceptional settranscendentalalgebraic

MSC classification

Secondary: 11J81: Transcendence (general theory)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 2 , October 2010 , pp. 322 - 327
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The second author is partially supported by FEMAT. The third author is supported by a Harrington Fellowship.

References

[1]Mahler, K., ‘Arithmetic properties of lacunary power series with integral coefficients’, J. Aust. Math. Soc. 168 (1965), 200–227.Google Scholar
[2]Mahler, K., Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976).Google Scholar
[3]Stäckel, P., ‘Ueber arithmetische Eigenschaften analytischer Functionen’, Math. Ann. 46(4) (1895), 513–520.CrossRefGoogle Scholar
[4]Stäckel, P., ‘Arithmetische Eigenschaften analytischer Functionen’, Acta Math. 25 (1902), 371–383.CrossRefGoogle Scholar
[5]Surroca, A., ‘Valeurs algébriques de fonctions transcendantes’, Int. Math. Res. Not. (2006), Art. ID 16834, 31 pp.Google Scholar
[6]Waldschmidt, M., ‘Algebraic values of analytic functions’, Proceedings of the International Conference on Special Functions and their Applications (Chennai, 2002), J. Comput. Appl. Math. 160(1–2) (2003), 323–333.Google Scholar