Applications of the Hasse-Weil bound to permutation polynomials

Riemann's hypothesis on function fields over a finite field implies the Hasse-Weil bound for the number of zeros of an absolutely irreducible bi-variate polynomial over a finite field. The Hasse-Weil bound has extensive applications in the arithmetic of finite fields. In this paper, we use the Hasse-Weil bound to prove two results on permutation polynomials over Fq where q is sufficiently large. To facilitate these applications, the absolute irreducibility of certain polynomials in Fq[X,Y] is established.