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Estimates for character sums with various convolutions

Volume 179 / 2017

Brandon Hanson 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 $p$.

Authors

  • Brandon HansonMathematics Department
    Pennsylvania State University
    University Park, PA 16802, U.S.A.
    e-mail

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