Geodesic
On Arithmetic Properties of the Taylor Series of Rational Functions
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 378-382

Voir la notice de l'article provenant de la source Cambridge University Press

Pólya (3) has shown that if bn is a sequence of algebraic integers and is a rational function, then so is . This result was generalized by Uchiyama (5) who showed that one may replace the assumption that the bn are algebraic integers by the assumption that the bn lie in a finitely generated submodule of the complex numbers, and by the author (1) who showed that if p is a non-zero polynomial with complex coefficients and if bn is a sequence of algebraic integers such that is a rational function, then so is . Our aim in this note is to give a common generalization of all of these theorems. 
Cantor, David G. On Arithmetic Properties of the Taylor Series of Rational Functions. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 378-382. doi: 10.4153/CJM-1969-039-9
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[1] 1. Cantor, D., On arithmetic properties of coefficients of rational functions, Pacific J. Math. 15 (1965), 55–58. Google Scholar

[2] 2. Lang, S., Introduction to algebraic geometry (Interscience, New York, 1958). Google Scholar

[3] 3. Pôlya, G., Arithmetische Eigenschaften der Reihenentwicklungen, J. Reine Angew. Math. 151 (1921), 1–31. Google Scholar

[4] 4. Salem, R., Algebraic numbers and Fourier analysis (D. C. Heath, Boston, Massachusetts, 1963). Google Scholar

[5] 5. Uchiyama, S., On a theorem of G. Pôlya, Proc. Japan Acad. 41 (1965), 517–520. Google Scholar

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