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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.11570 |
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| _version_ | 1866915065728335872 |
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| author | Murase, Atsushi Narita, Hiro-aki |
| author_facet | Murase, Atsushi Narita, Hiro-aki |
| contents | We investigate the theta correspondence of cusp forms for the dual pair $(O^*(4),{\mathrm Sp}(1,1))$ originally introduced by Tsuneo Arakawa in the non-adelic setting. We call this Arakawa lifting. In this paper, reformulating the theta correspondence in the adelic setting, we provide commutation relations of Hecke operators satisfied by Arakawa lifting at all non-Archimedean places, which is referred to as Eichler commutation relations for classical modular forms. Their Archimedean analogue is also given in terms of reproducing kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11570 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Arakawa lifting Part I: Eichler commutation relations Murase, Atsushi Narita, Hiro-aki Number Theory 11F55, 11F66 We investigate the theta correspondence of cusp forms for the dual pair $(O^*(4),{\mathrm Sp}(1,1))$ originally introduced by Tsuneo Arakawa in the non-adelic setting. We call this Arakawa lifting. In this paper, reformulating the theta correspondence in the adelic setting, we provide commutation relations of Hecke operators satisfied by Arakawa lifting at all non-Archimedean places, which is referred to as Eichler commutation relations for classical modular forms. Their Archimedean analogue is also given in terms of reproducing kernels. |
| title | On the Arakawa lifting Part I: Eichler commutation relations |
| topic | Number Theory 11F55, 11F66 |
| url | https://arxiv.org/abs/2412.11570 |