Geodesic
On Multiple Zeros of a Partial Theta Function
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 84-88.

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We consider the partial theta function $\theta (q,x):=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j$, where $x\in \mathbb{C}$ is a variable and $q\in \mathbb{C}$, $0|q|1$, is a parameter. We show that, for any fixed $q$, if $\zeta$ is a multiple zero of the function $\theta (q,\cdot)$, then $|\zeta |\le 8^{11}$.
Keywords: partial theta function, multiple zero, series. 
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V. P. Kostov. On Multiple Zeros of a Partial Theta Function. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 84-88. http://geodesic.mathdoc.fr/item/FAA_2016_50_2_a7/

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