# On generating functions for cubic polynomials

## Algebra and Number Theory Seminar

## Meeting Details

For more information about this meeting, contact Allyson Borger, Kirsten Eisentraeger, Jack Huizenga, Mihran Papikian, Ae Ja Yee, John Lesieutre.

**Speaker:** Bob Vaughan, PSU

**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.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/26/2019

**Time:** 11:00am - 11:50am