A functional bound for Young's cosine polynomial (Q2179849)

Young's inequality asserts that \(1+\sum_{k=1}^{n}\frac{\cos k\theta}{k}>0\) for all \(n\in\mathbb{N}\) and \(\theta\in(0,\pi).\) The paper under review is devoted to the following stronger result: \(\frac{5}{6}+\sum_{k=1}^{n}\frac{\cos k\theta}{k}\geq\frac{1}{4}(1+\cos\theta)^{2}\) for all \(n\geq2\) and \(\theta\in(0,\pi).\) Equality occurs if and only if \(n=2\) and \(\theta=\pi-\arccos\frac{1}{3}.\)