Zeros of Normalized Sections of Non Convergent Power Series

  • Alberto DayanEmail author


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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Authors and Affiliations

  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA

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