  We use the Langlands--Shahidi method in order to define the Shahidi gamma
factor for a pair of irreducible generic representations of
$\operatorname{GL}_n\left(\mathbb{F}_q\right)$ and
$\operatorname{GL}_m\left(\mathbb{F}_q\right)$. We prove that the Shahidi gamma
factor is multiplicative and show that it is related to the
Jacquet--Piatetski-Shapiro--Shalika gamma factor. As an application, we prove a
converse theorem based on the absolute value of the Shahidi gamma factor, and
improve the converse theorem of Nien. As another application, we give explicit
formulas for special values of the Bessel function of an irreducible generic
representation of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$.

Representation Theory;Number Theory