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arXiv · 2408.13682

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

Jared Duker Lichtman·Alexandru Pascadi
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Abstract

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.

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Jared Duker Lichtman, Alexandru Pascadi. 2024-08-24. Density theorems for $\text{GL}_n$ via Rankin-Selberg $L$-functions. https://arxiv.org/abs/2408.13682

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