Generic polynomials for cyclic function field extensions over certain finite fields

Abstract

In this paper, we find all the generic polynomials for geometric $\ell$-cyclic function field extensions over the finite fields ${\mathbb{F}}_q$ where $q=p^n$, $p$ prime integer such that $q\equiv -1\mathrm{mod}\ell$ and $(\ell ,p)=1$.

16 pages