On the uniform distribution of Gauss sums and Jacobi sums

Let F be a finite held with q elements, let Psi be a non-trivial additive character of F+, and chi, rho be the multiplicative characters of F-x. We denote by G (Psi, chi) the Gauss sums and by J (chi, rho) the Jacobi sums. In this paper, we consider the equidistribution properties of the following sequences in the interval [0, 1] as q --> infinity: {1/2 pi arg G (Psi, chi)}, Psi not equal Psi(0), chi not equal chi(0), and {1/2 pi arg J (chi, rho)}, chi not equal chi(0), rho not equal chi(0), chi(-1). We establish some equidistribution estimates with better error terms for them. Also are give moment estimates for G (Psi, chi) and J (chi, rho).