A domain free of the zeros of the partial theta function

DOI10.30970/MS.58.2.142-158arXiv2210.16214MaRDI QIDQ6415427

Vladimir P. Kostov

Publication date: 28 October 2022

Abstract: We prove that for $qin(0,1)$, the partial theta function $heta(q,x):=su{m}_{j=0}^{infty}{q}^{j(j+1)/2}{x}^j$ has no zeros in the closed domain $${ m Re}$xleq0cap|${ m Im}$$ and no real zeros $geq-5$.

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Other functions defined by series and integrals (33E20) One-variable calculus (26A06)

This page was built for publication: A domain free of the zeros of the partial theta function

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6415427)