On generating functions in additive number theory, II: Lower-order terms and applications to PDEs

Julia Brandes, Scott T. Parsell, Konstantinos Poulias +2

We obtain asymptotics for sums of the form $$\sum _{n=1}^{P}e({\alpha }_k{n}^k+{\alpha }_{1}n),$$ involving lower order main terms. As an application, we show that for almost all ${\alpha }_2\in [0,1)$ one…