Subconvexity Problem on $\operatorname{GL}_3$ over number fields: the twist aspect
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915812377362432 |
|---|---|
| author | Berta, Filippo |
| author_facet | Berta, Filippo |
| contents | Let $F$ denote a number field and let $\mathfrak{q}\subset O_F$ traverse a sequence of prime ideals with norm $N(\mathfrak{q}) \to \infty$ and for each $\mathfrak{q}$, let $χ\in \widehat{F^{\times}\setminus \mathbb{A}^\times}$ be a finite order character of conductor $\mathfrak{q}$. For a fixed unitary cuspidal automorphic representation $π$ of $\operatorname{GL}_3/F$ we show that \begin{equation*} L(π\otimes χ,\tfrac{1}{2})\ll \ N(\mathfrak{q})^{3/4-κ}.\end{equation*} holds for all $κ< \frac{1}{36}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subconvexity Problem on $\operatorname{GL}_3$ over number fields: the twist aspect Berta, Filippo Number Theory 11FF66, 11R42 Let $F$ denote a number field and let $\mathfrak{q}\subset O_F$ traverse a sequence of prime ideals with norm $N(\mathfrak{q}) \to \infty$ and for each $\mathfrak{q}$, let $χ\in \widehat{F^{\times}\setminus \mathbb{A}^\times}$ be a finite order character of conductor $\mathfrak{q}$. For a fixed unitary cuspidal automorphic representation $π$ of $\operatorname{GL}_3/F$ we show that \begin{equation*} L(π\otimes χ,\tfrac{1}{2})\ll \ N(\mathfrak{q})^{3/4-κ}.\end{equation*} holds for all $κ< \frac{1}{36}$. |
| title | Subconvexity Problem on $\operatorname{GL}_3$ over number fields: the twist aspect |
| topic | Number Theory 11FF66, 11R42 |
| url | https://arxiv.org/abs/2602.20095 |