# On generating functions for cubic polynomials

## Meeting Details

Abstract: Jointly with Julia Brandes, Scott Parsell, Constantinos Poulias and George Shakan we obtain more precise expressions than hitherto for the exponential sum $\sum_{n\le P} e(\alpha_1 n + \alpha_3 n^3).$ The original stimulus was an application in additive number theory. However there is also an application to PDEs, and in particular we completely solve a problem of Erdo\u gan and Shakan related to the fractal dimension of solutions of Airy's, Schroedinger's and the Korteweg-de Vries' equations.