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

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

2010-04-21

arxiv.org/abs/1004.3813v3

Int. J. Number Theory, vol. 7:7, p. 1807-1823 (2011)

Mathematics

Number Theory

16 pages; the application to irreducibility and the final example have been corrected

Scientific paper

10.1142/S1793042111004691

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.

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