Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds
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| Format: | Preprint |
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2024
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| _version_ | 1866911976314109952 |
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| author | Marshall, Simon Narita, Hiroaki Pitale, Ameya |
| author_facet | Marshall, Simon Narita, Hiroaki Pitale, Ameya |
| contents | We give an explicit formula for the Petersson norms of theta lifts from Maass cusp forms of level one to cusp forms on orthogonal groups O(1,8n+1). Our formula explicitly determines archimedean local factors of the norms. As an application, we obtain the injectivity of the lifting of Maass forms and bounds on the sup-norm of cusp forms on these orthogonal groups in terms of their Laplace eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds Marshall, Simon Narita, Hiroaki Pitale, Ameya Number Theory We give an explicit formula for the Petersson norms of theta lifts from Maass cusp forms of level one to cusp forms on orthogonal groups O(1,8n+1). Our formula explicitly determines archimedean local factors of the norms. As an application, we obtain the injectivity of the lifting of Maass forms and bounds on the sup-norm of cusp forms on these orthogonal groups in terms of their Laplace eigenvalues. |
| title | Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.04426 |