Hostname: page-component-76c49bb84f-xk4dl Total loading time: 0 Render date: 2025-07-13T03:40:26.781Z Has data issue: false hasContentIssue false
  • English
  • Français

On the optimality of certain estimates for algebraic values of analytic functions

Published online by Cambridge University Press:  09 April 2009

Isao Wakabayashi
Isao Wakabayashi
Affiliation:
Department of Mathematics, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove, by constructing a function with given parameters, that the estimate by G. V. Chudnovsky of the number of points at which a meromorphic function has algebraic Taylor coefficients is optimal. The construction is carried out by the use of interpolation series.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 400 - 414
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bertrand, D., ‘A transcendence criterion for meromorphic functions’, Transcendence theory: Advances and applications (Academic Press, London, 1977, PP. 187–193).Google Scholar
[2]Bertrand, D. and Waldschmidt, M., ‘On meromorphic functions of one complex variable having algebraic Laurent coefficients’, Bull. Austral. Math. Soc. 24 (1981), 247–267.CrossRefGoogle Scholar
[3]Cassels, J. W. S., An introduction to diophantine approximation (Hafner Publishing Company, New York, 1972).Google Scholar
[4]Chudnovsky, G. V., ‘Values of meromorphic functions of order 2’, Séminaire Delange—Pisot—Poitou, 19e année (1977/1978), n°45, 1–18.Google Scholar
[5]Chudnovsky, G. V., ‘A new method for the investigation of arithmetical properties of analytic functions’, Ann. of Math. 109 (1979), 353–376.CrossRefGoogle Scholar
[6]Schmidt, W. M., Approximation to algebraic numbers (Monographies de 1'Enseignement Math., 19, Université Genéve, 1972).Google Scholar
[7]Schneider, Th., Einführung in die transzendenten Zahlen (Grundlehren 81, Springer-Verlag, Berlin, Göttingen, Heidelberg, 1957).CrossRefGoogle Scholar
[8]Waldschmidt, M., Nombres transcendants (Lecture Notes in Math., 402, Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[9]Waldschmidt, M., ‘On functions of several variables having algebraic Taylor coefficients’, Transcendence theory: Advances and applications (Academic Press, London, 1977, pp. 169–186).Google Scholar