# The leading root of the partial theta function

@article{Sokal2012TheLR,
title={The leading root of the partial theta function},
author={Alan D. Sokal},
year={2012},
volume={229},
pages={2603-2621}
}
• A. Sokal
• Published 6 June 2011
• Mathematics
• Advances in Mathematics

### On a partial theta function and its spectrum

• V. Kostov
• Mathematics
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
• 2016
The bivariate series defines a partial theta function. For fixed q (∣q∣ < 1), θ(q, ·) is an entire function. For q ∈ (–1, 0) the function θ(q, ·) has infinitely many negative and infinitely many

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We consider the partial theta function θ(q, x) := ∑j=0∞qj(j+1)/2xj, where x ∈ ℂ is a variable and q ∈ ℂ, 0 < |q| < 1, is a parameter. We show that, for any fixed q, if ζ is a multiple zero of the

### 2 0 N ov 2 01 9 Two properties of the partial theta function

For the partial theta function θ(q, z) := ∑ ∞ j=0 q z, q, z ∈ C, |q| < 1, we prove that its zero set is connected. This set is smooth at every point (q, z) such that z is a simple or double zero of

### On the Complex Conjugate Zeros of the Partial Theta Function

• V. P. Rostov
• Mathematics, Philosophy
Functional Analysis and Its Applications
• 2019

### Stabilization of the asymptotic expansions of the zeros of a partial theta function

The bivariate series $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ defines a {\em partial theta function}. For fixed $q$ ($|q|<1$), $\theta (q,.)$ is an entire function. We prove a property of