The Theorem of Jentzsch-Szegő on an analytic curve. Application to the irreducibility of truncations of power series - Mathematics > Number TheoryReport as inadecuate




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Abstract: The theorem of Jentzsch-Szeg\H{o} describes the limit measure of a sequenceof discrete measures associated to the zeroes of a sequence of polynomials inone variable. Following the presentation of this result by Andrievskii andBlatt in their book, we extend this theorem to compact Riemann surfaces, thento analytic curves over an ultrametric field. The particular case of theprojective line over an ultrametric field gives as corollaries informationabout the irreducibility of the truncations of a power series in one variable.



Author: Antoine Chambert-Loir

Source: https://arxiv.org/







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