Evaluation of Some Sums of Polynomials in F q [ t ]

Abstract

We prove the polynomial analogues of some Liouville identities from elementary number theory. Consequently several sums defined over the finite fields ${\mathbb{F}}_q[t]$ are evaluated by combining the results obtained and some of the results from sums of reciprocals of polynomials over ${\mathbb{F}}_q[t]$.