This article is cited in 6 papers

Brief communications

On Multiple Zeros of a Partial Theta Function

V. P. Kostov

Université de Nice, Laboratoire de Mathématiques

Abstract: We consider the partial theta function $\theta (q,x):=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j$, where $x\in \mathbb{C}$ is a variable and $q\in \mathbb{C}$, $0<|q|<1$, is a parameter. We show that, for any fixed $q$, if $\zeta$ is a multiple zero of the function $\theta (q,\cdot)$, then $|\zeta |\le 8^{11}$.

Keywords: partial theta function, multiple zero, series.

UDC: 517.531.55

Received: 29.09.2015

DOI: 10.4213/faa3238

 English version: Functional Analysis and Its Applications, 2016, 50:2, 153–156

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