The closest to $0$ spectral number of the partial theta function

Abstract

The {\em spectrum} of the partial theta function $\theta :={\sum }_{j=0}^{\infty }{q}^{j(j+1)/2}{x}^j$ is the set of values of $q\in \mathbb{C}$, $0<|q|<1$, for which $\theta (q,.)$ has a multiple zero. We show that the only element of the spectrum belonging to the disk ${\mathbb{D}}_{0.31}$ is $0.3092493386\dots$.

Cited by in corpus (2)

• On the conditions for a special entire function relative to the partial theta-function and the Euler function to belong to the Laguerre-Pólya class
• On the zero set of the partial theta function