On the location of the complex conjugate zeros of the partial theta function
Abstract
We prove that for any \(q\in (0,1)\), all complex conjugate pairs of zeros of the partial theta function \(\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j\) with non-negative real part belong to the half-annulus \(\{{\rm Re}(x)\geq 0,~1
Fields of Study & Subjects
Advanced Mathematical Identities
Mathematical functions and polynomials
Analytic Number Theory Research
Publication details
- Journal / source
- Serdica Mathematical Journal
- Publisher
- Institute of Mathematics and Informatics Bulgarian Academy of Sciences
- Volume
- 52
- Issue
- 1
- Publication date
- 13 April 2026
- Language
- EN