Equidistribution and independence of Gauss sums

We prove a general independent equidistribution result for Gauss sums associated to n monomials in r variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and Jacobi sums. As an application, we show that any relation satisfied by these Gauss sums must be a combination of the conjugation relation G ( chi ) G ( chi ) = +/- q , Galois conjugation invariance and the Hasse -Davenport product formula. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).