Estimates for Character Sums with Various Convolutions

Abstract

We provide estimates for sums of the form \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}χ(a+b+c)\right|\] and \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\sum_{d\in D}χ(a+b+cd)\right|\] when $A,B,C,D\subset {\mathbb{F}}_p$, the field with $p$ elements and $\chi$ is a non-trivial multiplicative character modulo $p$.

arXiv comment17 pages