The generalized Ramanujan conjecture for globally generic cuspidal representations of exceptional groups over function fields

Theorem 1.1: for $G$ split connected adjoint absolutely simple of type $G_2,F_4,E_6,E_7$ or $E_8$ over a global function field, every complex globally generic cuspidal automorphic representation is tempered at every place. The companion (September 24) gives temperedness at unramified places for all split adjoint absolutely simple groups from genericity at one unramified place. Nothing is claimed over number fields, for non-generic representations, or for ramified places of classical groups beyond what Lomeli already proved.

Theorem 1.1: for $G$ split connected adjoint absolutely simple of type $G_2,F_4,E_6,E_7$ or $E_8$ over a global function field, every complex globally generic cuspidal automorphic representation is tempered at every place. The companion (September 24) gives temperedness at unramified places for all split adjoint absolutely simple groups from genericity at one unramified place. Nothing is claimed over number fields, for non-generic representations, or for ramified places of classical groups beyond what Lomeli already proved.