  We recall the relation between Zeta function representation of groups and
two-dimensional topological Yang-Mills theory through Mednikh formula. We prove
various generalisations of Mednikh formulas and define generalization of Zeta
functions representations of groups. We compute some of these functions in the
case of the finite group $GL(2, {\mathbb F}_q)$ and $PGL(2,{\mathbb F}_q).$ We
recall the table characters of these groups for any $q$, compute the
Frobenius-Schur indicator of their irreducible representations and give the
explicit structure of their fusion rings
