Density theorems for ${\text{GL}}_n$ via Rankin-Selberg $L$-functions

We obtain density theorems for cuspidal automorphic representations of ${\text{GL}}_n$ over $\mathbb{Q}$ 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.