Estimates for character sums with various convolutions
Volume 179 / 2017
Acta Arithmetica 179 (2017), 133-146
MSC: Primary 11L40.
DOI: 10.4064/aa8404-5-2017
Published online: 7 July 2017
Abstract
We provide estimates for sums of the form \[ \Bigl|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\chi(a+b+c)\Bigr| \quad \text{and}\quad \Bigl|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\sum_{d\in D}\chi(a+b+cd)\Bigr| \] when $A,B,C,D\subset \mathbb F_p$, the field with $p$ elements, and $\chi$ is a non-trivial multiplicative character modulo $p$.
