Equidistribution of exponential sums

Many exponential sums, such as Gauss sums or Kloosterman sums, appear as the Fourier transform of the trace function of an $l$-adic sheaf on a algebraic group over a finite field. I will discuss equidistribution results for these sums when the $l$-adic sheaf is fixed but the character with respect to which the Fourier transform is taken varies.