Poles of Eisenstein series on general linear groups induced from two Speh representations
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913568040943616 |
|---|---|
| author | Ginzburg, David Soudry, David |
| author_facet | Ginzburg, David Soudry, David |
| contents | We determine the poles of the Eisenstein series on a general linear group, induced from two Speh representations, $Δ(τ,m_1)|\cdot|^s\timesΔ(τ,m_2)|\cdot|^{-s}$, $Re(s)\geq 0$, where $τ$ is an irreducible, unitary, cuspidal, automorphic representation of $GL_n({\bf A})$. The poles are simple and occur at $s=\frac{m_1+m_2}{4}-\frac{i}{2}$, $0\leq i\leq min(m_1,m_2)-1$. Our methods also show that when $m_1=m_2$, the above Eisenstein series vanish at s=0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poles of Eisenstein series on general linear groups induced from two Speh representations Ginzburg, David Soudry, David Representation Theory We determine the poles of the Eisenstein series on a general linear group, induced from two Speh representations, $Δ(τ,m_1)|\cdot|^s\timesΔ(τ,m_2)|\cdot|^{-s}$, $Re(s)\geq 0$, where $τ$ is an irreducible, unitary, cuspidal, automorphic representation of $GL_n({\bf A})$. The poles are simple and occur at $s=\frac{m_1+m_2}{4}-\frac{i}{2}$, $0\leq i\leq min(m_1,m_2)-1$. Our methods also show that when $m_1=m_2$, the above Eisenstein series vanish at s=0. |
| title | Poles of Eisenstein series on general linear groups induced from two Speh representations |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.23026 |