The Theorem of Jentzsch--Szegö on an analytic curve. Application to the irreducibility of truncations of power series

Abstract : The theorem of Jentzsch--Szeg\H{o} 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.
Type de document :
Article dans une revue
International Journal of Number Theory, World Scientific Publishing, 2011, 7 (7), pp.1807-1823. 〈10.1142/S1793042111004691〉
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Contributeur : Marie-Annick Guillemer <>
Soumis le : mardi 14 juin 2011 - 16:30:08
Dernière modification le : samedi 23 septembre 2017 - 01:12:26

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Antoine Chambert-Loir. The Theorem of Jentzsch--Szegö on an analytic curve. Application to the irreducibility of truncations of power series. International Journal of Number Theory, World Scientific Publishing, 2011, 7 (7), pp.1807-1823. 〈10.1142/S1793042111004691〉. 〈hal-00600373〉

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