Density theorems for $\text{GL}_n$ via Rankin-Selberg $L$-functions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912000981860352 |
|---|---|
| author | Lichtman, Jared Duker Pascadi, Alexandru |
| author_facet | Lichtman, Jared Duker Pascadi, Alexandru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density theorems for $\text{GL}_n$ via Rankin-Selberg $L$-functions Lichtman, Jared Duker Pascadi, Alexandru Number Theory Representation Theory 11F70, 11F66, 11F30, 11R42 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. |
| title | Density theorems for $\text{GL}_n$ via Rankin-Selberg $L$-functions |
| topic | Number Theory Representation Theory 11F70, 11F66, 11F30, 11R42 |
| url | https://arxiv.org/abs/2408.13682 |