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arXiv · 2210.16214

A domain free of the zeros of the partial theta function

Vladimir Petrov Kostov
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Abstract

We prove that for $q\in (0,1)$, the partial theta function $θ(q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed domain $\{ \{ |x|\leq 3\} \cap \{${\rm Re}$x\leq 0\} \cap \{ |${\rm Im}$x|\leq 3/\sqrt{2}\} \} \subset \mathbb{C}$ and no real zeros $\geq -5$.

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Vladimir Petrov Kostov. 2022-10-28. A domain free of the zeros of the partial theta function. https://arxiv.org/abs/2210.16214

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