A converse theorem for Borcherds products in signature $(2,2)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929415022182400 |
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| author | Bieker, Patrick Kiefer, Paul |
| author_facet | Bieker, Patrick Kiefer, Paul |
| contents | We show that a modular unit on two copies of the upper half-plane is a Borcherds product if and only if its boundary divisor is a special boundary divisor. Therefore, we define a subspace of the space of invariant vectors for the Weil representation which maps surjectively onto the space of modular units that are Borcherds products. Moreover, we show that every boundary divisor of a Borcherds product can be obtained in this way. As a byproduct we obtain new identities of eta products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A converse theorem for Borcherds products in signature $(2,2)$ Bieker, Patrick Kiefer, Paul Number Theory 11F20, 11F27, 11F37 We show that a modular unit on two copies of the upper half-plane is a Borcherds product if and only if its boundary divisor is a special boundary divisor. Therefore, we define a subspace of the space of invariant vectors for the Weil representation which maps surjectively onto the space of modular units that are Borcherds products. Moreover, we show that every boundary divisor of a Borcherds product can be obtained in this way. As a byproduct we obtain new identities of eta products. |
| title | A converse theorem for Borcherds products in signature $(2,2)$ |
| topic | Number Theory 11F20, 11F27, 11F37 |
| url | https://arxiv.org/abs/2407.06610 |