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Fatou's theorems on power series and their multivariate extensions
【2019.10.8 3:30pm, N202】

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 2019-9-29 

  Colloquia & Seminars 

  Speaker

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

  Title

Fatou's theorems on power series and their multivariate extensions

  Time

2019.10.08 15:30-17:30 

  Venue

N202

  Abstract

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.  

  Affiliation

 

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