No zeros of the partial theta function in the unit disk

Authors

DOI:

https://doi.org/10.60063/gsu.fmi.111.129-137

Keywords:

Jacobi theta function, Jacobi triple product, partial theta function

Abstract

We prove that for $q\in (-1,0)\cup (0,1)$, the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ has no zeros in the closed unit disk.

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Published

2024-12-04

How to Cite

Kostov, V. (2024). No zeros of the partial theta function in the unit disk. Ann. Sofia Univ. Fac. Math. And Inf., 111, 129–137. https://doi.org/10.60063/gsu.fmi.111.129-137

Issue

Vol. 111 (2024): Ann. Sofia Univ. Fac. Math. and Inf.

Section

Articles