On Multiple Zeros of a Partial Theta Function

V. P. Kostov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 2, pp. 84-88

Résumé

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 $|\zeta |\le 8^{11}$.

Détail

Keywords: partial theta function, multiple zero, series.