  The bivariate series $\theta (q,x):=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j$
defines a {\em partial theta function}. For fixed $q$, $\theta (q,.)$ is an
entire function. We show that for $|q|\leq 0.108$ the function $\theta (q,.)$
has no multiple zeros.
