a product of Artin $L$-functions, the latter conjecture is a consequence of the Artin conjecture. This relationship is one display in Flicker’s conditional result. For more details about this relationship, see [@JngR].

In the case when the global field is ${\mathbb{Q}},$ Conjecture \[conj: adjoint GL3 is entire\] may also be viewed from the point of view of the Selberg class. We recall that the Selberg class is a class of meromorphic functions ${\mathbb{C}}\to {\mathbb{C}}$ introduced by Selberg in [@Selberg]. For $\pi$ a cuspidal automorphic representation of ${{\mathrm{GL}}}_n({\mathbb{A}}),$ the finite $L$-function $L_f (s, \pi \times {\widetilde}\pi)$ will be an element of the Selberg class, unless $\pi$ is a counterexample to the Ramanujan conjecture. It then would follow from the conjectures in [@Selberg] that $L_f(s, \pi \times {\widetilde}\pi)$ must be the product of the Riemann zeta function and another element of the Selberg class (cf. remark ii at the bottom of p. 370 of [@Selberg]). In other words it would follow that $L_f(s, \pi, {{\mathrm{Ad}}})$ is itself an element of the Selberg class. But then it must be entire since elements of the Selberg class have no poles except possibly at one.

Main results
------------

For $n>2$ the adjoint $L$-function of ${{\mathrm{GL}}}_n$ 