Zeros of Normalized Sections of Non Convergent Power Series
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.
 Publication:

arXiv eprints
 Pub Date:
 January 2019
 arXiv:
 arXiv:1901.08721
 Bibcode:
 2019arXiv190108721D
 Keywords:

 Mathematics  Complex Variables