Equidistribution and independence of Gauss sums

Abstract

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 $G(\chi )G(\overline{\chi })=\pm q$, Galois conjugation invariance and the Hasse-Davenport product formula.