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On meromorphic functions of one complex variable having algebraic Laurent coefficients

Published online by Cambridge University Press:  17 April 2009

Daniel Bertrand  and
Michel Waldschmidt
Daniel Bertrand
Affiliation:
Université de Nice, Mathématiques - Parc Valrose, 06034 Nice Cedex, France;
Michel Waldschmidt
Affiliation:
Université Pierre et Marie Curie, Mathématiques T. 45–46, 75230 Paris Cedex 05, France.
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Abstract

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We study the set of points at which two algebraically independent meromorphic functions have algebraic coefficients in their Laurent expansions. After a survey of the present knowledge in this field, we obtain two general transcendence criteria which sharpen previous results of Straus, Schneider and Lang. As a corollary, we give a new proof, based on Gel'fond's method, of some of Siegel's results on E-functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 2 , October 1981 , pp. 247 - 267
Copyright
Copyright © Australian Mathematical Society 1981

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