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arXiv · 1605.05469

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

Vladimir Kostov
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Abstract

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

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Vladimir Kostov. 2016-05-18. The closest to $0$ spectral number of the partial theta function. https://arxiv.org/abs/1605.05469

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