Zeros of Normalized Sections of Non Convergent Power Series

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A well known result due to Carlson (C R Acad Sci Paris 178:1677–1680, 1924) affirms that a power series with finite and positive radius of convergence R has no Ostrowski gaps if and only if the sequence of zeros of its nth sections is asymptotically equidistributed to \(\partial \mathbb {D}_R\). Here we extend this characterization to those power series with null radius of convergence, modulo some necessary normalizations of the sequence of the sections of f.

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    We may choose any \(1<r<\infty \) if G is null.


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Correspondence to Alberto Dayan.

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Research supported by Starting Grant (StG), PE1, ERC-2012-StG-20111012.

Communicated by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Dayan, A. Zeros of Normalized Sections of Non Convergent Power Series. Complex Anal. Oper. Theory 14, 10 (2020) doi:10.1007/s11785-019-00963-6

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