We use the Langlands–Shahidi method in order to define the Shahidi
gamma factor for a pair of irreducible generic representations of
${\mathrm{GL}}_{n}({\mathbb{\mathbb{F}}}_{q})$ and
${\mathrm{GL}}_{m}({\mathbb{\mathbb{F}}}_{q})$. 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
${\mathrm{GL}}_{n}({\mathbb{\mathbb{F}}}_{q})$.