No zeros of the partial theta function in the unit disk

We prove that for $q\in (-1,0)\cup (0,1)$, the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed unit disk.

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Publication Details

Journal
Annual of Sofia University St Kliment Ohridski Faculty of Mathematics and Informatics
Published
2024-12-04
DOI
https://doi.org/10.60063/gsu.fmi.111.129-137
Primary Topic
Analytic and geometric function theory
Type
article
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article

No zeros of the partial theta function in the unit disk

Vladimir Petrov Kostov
Annual of Sofia University St Kliment Ohridski Faculty of Mathematics and Informatics
Analytic and geometric function theory
article

No zeros of the partial theta function in the unit disk

Vladimir Petrov Kostov
article en

Abstract

We prove that for $q\in (-1,0)\cup (0,1)$, the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed unit disk.

Annual of Sofia University St Kliment Ohridski Faculty of Mathematics and InformaticsVol. 111
Reduced inequalities
Openalex Percentile: Top 66%
Analytic and geometric function theory
DOIOpen Access PDFOpenAlex
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No zeros of the partial theta function in the unit disk — Vladimir Petrov Kostov · Annual of Sofia University St Kliment Ohridski Faculty of Mathematics and Informatics (2024) | TGRS Research Map | TGRS