On a conjecture of Faulhuber and Steinerberger on the logarithmic derivative of $\vartheta_4$

Abstract

Faulhuber and Steinerberger conjectured that the logarithmic derivative of $\vartheta_4$ has the property that $y^2\,\vartheta_4'(y)/\vartheta_4(y)$ is strictly decreasing and strictly convex. In this small note, we prove this conjecture.