Density theorems for GLₙ via Rankin-Selberg L-functions

We obtain density theorems for cuspidal automorphic representations of GLₙ over Q which fail the generalized Ramanujan conjecture at some place. We depart from previous approaches based on Kuznetsov-type trace formulae, and instead rely on L-function techniques. This improves recent results of Blomer near the threshold of the pointwise bounds.