Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.20653 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912505185435648 |
|---|---|
| author | Jiang, Yujiao |
| author_facet | Jiang, Yujiao |
| contents | We prove Hypothesis H in full generality for ${\rm GL}_n$ over any number field. This result is a consequence of our stronger effective bound on Euler products involving Rankin--Selberg coefficients at prime ideal powers. The proof rests on a new analytic method, which employs a power sieve over number fields and an iterative argument to bypass the functoriality barrier that had restricted prior results to $n\leq 4$. As applications, we unconditionally establish the GUE statistics for automorphic $L$-function zeros, provide the first effective polynomial bound for the strong multiplicity one problem for coefficients, and resolve the Selberg orthogonality conjecture with stronger error terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hypothesis H of Rudnick and Sarnak Jiang, Yujiao Number Theory We prove Hypothesis H in full generality for ${\rm GL}_n$ over any number field. This result is a consequence of our stronger effective bound on Euler products involving Rankin--Selberg coefficients at prime ideal powers. The proof rests on a new analytic method, which employs a power sieve over number fields and an iterative argument to bypass the functoriality barrier that had restricted prior results to $n\leq 4$. As applications, we unconditionally establish the GUE statistics for automorphic $L$-function zeros, provide the first effective polynomial bound for the strong multiplicity one problem for coefficients, and resolve the Selberg orthogonality conjecture with stronger error terms. |
| title | On Hypothesis H of Rudnick and Sarnak |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.20653 |