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<p>Polya–Carlson theorem asserts that if a power series with integer coefficients and convergence radius 1 can be extended holomorphically out of the unit disc, it must represent a rational function. In this note, we give a generalization of this result to multivariate case and give an application to rationality theorem about D-finite power series.</p>

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An Analytic Proof of Multivariate Polya–Carlson Theorem

  • 期刊论文

  • 发表日期：

    2025年11月15日

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  • Tianlong Yu

摘要

Polya–Carlson theorem asserts that if a power series with integer coefficients and convergence radius 1 can be extended holomorphically out of the unit disc, it must represent a rational function. In this note, we give a generalization of this result to multivariate case and give an application to rationality theorem about D-finite power series.