Pullback of arithmetic theta series and its modularity for unitary Shimura curves
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_ | 1866918156002394112 |
|---|---|
| author | He, Qiao Shi, Yousheng Yang, Tonghai |
| author_facet | He, Qiao Shi, Yousheng Yang, Tonghai |
| contents | This paper is a complement of the modularity result of Bruinier, Howard, Kudla, Rapoport and Yang (BHKRY) for the special case $U(1,1)$ not considered there. The main idea to embed a $U(1, 1)$ Shimura curve to many $U(n-1, 1)$ Shimura varieties for big $n$, and prove a precise pullback formula of the generating series of arithmetic divisors. Afterwards, we use the modularity result of BHKRY together with existence of non-vanishing of classical theta series at any given point in the upper half plane to prove the modulartiy result on $U(1, 1)$ Shimura curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pullback of arithmetic theta series and its modularity for unitary Shimura curves He, Qiao Shi, Yousheng Yang, Tonghai Number Theory 11G15, 11F11, 11F30 This paper is a complement of the modularity result of Bruinier, Howard, Kudla, Rapoport and Yang (BHKRY) for the special case $U(1,1)$ not considered there. The main idea to embed a $U(1, 1)$ Shimura curve to many $U(n-1, 1)$ Shimura varieties for big $n$, and prove a precise pullback formula of the generating series of arithmetic divisors. Afterwards, we use the modularity result of BHKRY together with existence of non-vanishing of classical theta series at any given point in the upper half plane to prove the modulartiy result on $U(1, 1)$ Shimura curves. |
| title | Pullback of arithmetic theta series and its modularity for unitary Shimura curves |
| topic | Number Theory 11G15, 11F11, 11F30 |
| url | https://arxiv.org/abs/2403.04566 |