English

A multivariate version of Polya-Carlson theorem

Complex Variables 2023-12-27 v4

Abstract

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.

Keywords

Cite

@article{arxiv.2312.00428,
  title  = {A multivariate version of Polya-Carlson theorem},
  author = {Tianlong Yu},
  journal= {arXiv preprint arXiv:2312.00428},
  year   = {2023}
}
R2 v1 2026-06-28T13:38:09.414Z