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arXiv · 1902.01726

On the complex conjugate zeros of the partial theta function

Vladimir Petrov Kostov
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Abstract

We prove that 1) for any $q\in (0,1)$, all complex conjugate pairs of zeros of the partial theta function $θ(q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ belong to the set $\{$~Re\,$x\in (-5792.7,0),$~$|$Im\,$x|<132~\}$ $\cup$ $\{ ~|x|<18~\}$ and 2) for any $q\in (-1,0)$, they belong to the rectangle $\{$~$|$Re\,$x|< 364.2,$~$|$Im\,$x|<132~\}$.

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Vladimir Petrov Kostov. 2019-02-05. On the complex conjugate zeros of the partial theta function. https://arxiv.org/abs/1902.01726

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