Zeros of Normalized Sections of Non Convergent Power Series

Alberto Dayan

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arXiv · 1901.08721

Zeros of Normalized Sections of Non Convergent Power Series

Alberto Dayan

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Abstract

A well known result due to Carlson 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 {|z|=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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Alberto Dayan. 2019-01-25. Zeros of Normalized Sections of Non Convergent Power Series. https://arxiv.org/abs/1901.08721

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