Zeros of Normalized Sections of Non Convergent Power Series

Alberto Dayan

doi:10.1007/s11785-019-00963-6

Zeros of Normalized Sections of Non Convergent Power Series

Alberto Dayan^*

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

Washington University in St. Louis (WUSTL)

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Resum

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 ∂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.

Idioma original	Anglès
Número d’article	10
Revista	Complex Analysis and Operator Theory
Volum	14
Número	1
DOIs	https://doi.org/10.1007/s11785-019-00963-6
Estat de la publicació	Publicada - 1 de febr. 2020

Accés al document

10.1007/s11785-019-00963-6

Com citar-ho

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abstract = "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 ∂DR. 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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AB - 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 ∂DR. 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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