The trigonometric polynomial on sums of two squares, an additive problem and generalisation

Olivier Ramare, GK Viswanadham

Let $B$ be the set of odd integers that are sums of two coprime squares. We prove that the trigonometric polynomial $S(\alpha ;N)={\sum }_{b\in B,b\le N}e(b\alpha )$ satisfies \[ \frac{S(α; N)}…