Geodesic
Zeros of Sequences of Partial Sums and Overconvergence
Serdica Mathematical Journal, Tome 34 (2008) no. 2, pp. 467-482

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We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated.
Keywords: Overconvergence, Hadamard-Ostrowski Gaps, Equilibrium Measure 
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     author = {Kovacheva, Ralitza K.},
     title = {Zeros of {Sequences} of {Partial} {Sums} and {Overconvergence}},
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Kovacheva, Ralitza K. Zeros of Sequences of Partial Sums and Overconvergence. Serdica Mathematical Journal, Tome 34 (2008) no. 2, pp. 467-482. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_2_a6/