中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

多复变与复几何学术讨论班

Some Topics in Several Complex Variables

报告人陈绍示 (中科院数学与系统科学研究院, 数学机械化重点实验室)

 Fatou's theorems on power series and their multivariate extensions

  2019.10.08(星期, 15:30-17:30

  数学院南楼N202

    In 1906, Fatou proved two rational-transcendental dichotomy theorems on power series: (1) a power series with finitely distinct coefficients is either rational or transcendental; (2) a power series with integer coefficients and of radius of convergence 1 is either rational or transcendental. Fatou's theorems were later extended in the work of other mathematicians, such as Polya, Carlson, and Szego. The classical results are mainly focusing on the univariate power series. In this talk, we will present some multivariate extensions of Fatou's theorems for D-finite power series.

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