Representations of the Character Groups of Fq

Abstract

We give non-trivial unitary representations of the character groups of a finite field Fq. With the representation properties we deduce some results on character sums, and with the unitarity we obtain non-trivial estimates for the incomplete sums \(\sum_{\nu =1}^k\ G(\chi_i\chi _\nu^{- 1},\psi);1\leq k <q\).