解析曲线上的Jentzsch-SzegIgnon定理.幂级数截断不可约性的应用
The Theorem of Jentzsch--Szegő on an analytic curve. Application to the irreducibility of truncations of power series
摘要：
定理Jentzsch-SzegIgn描述了极限措施的一系列离散措施相关联的零序列的多项式在一个变量。继Andrievskii和Blatt在他们的书中提出这个结果之后，我们将这个定理推广到紧致黎曼曲面，然后推广到超度量场上的解析曲线。超距离域上的投影线的特殊情况给出了关于单变量幂级数截断的不可约性的推论。
英文摘要：
The theorem of Jentzsch--Szegő describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann surfaces, then to analytic curves over an ultrametric field. The particular case of the projective line over an ultrametric field gives as corollaries information about the irreducibility of the truncations of a power series in one variable.
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