ON SOME MULTIPLE CHARACTER SUMS

摘要

We improve a recent result of B. Hanson [Estimates for character sums with various convolutions. Preprint, 2015, arXiv: 1509.04354] on multiplicative character sums with expressions of the type a + b + cd and variables a, b, c, d from four distinct sets of a finite field. We also consider similar sums with a + b(c + d). Our new bounds rely on some recent advances in additive combinatorics.