Injectivity of the genus 1 Kudla-Millson lift on locally symmetric spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918124586008576 |
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| author | Metzler, Ingmar Zuffetti, Riccardo |
| author_facet | Metzler, Ingmar Zuffetti, Riccardo |
| contents | Let $L$ be an even indefinite lattice. We show that if $L$ splits off a hyperbolic plane and a scaled hyperbolic plane, then the Kudla-Millson lift of genus $1$ associated to $L$ is injective. Our result includes as special cases all previously known injectivity results on the whole space of elliptic cusp forms available in the literature. In particular, we also consider the Funke-Millson twist of the lift. Further, we provide geometric applications on locally symmetric spaces of orthogonal type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00572 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Injectivity of the genus 1 Kudla-Millson lift on locally symmetric spaces Metzler, Ingmar Zuffetti, Riccardo Number Theory Algebraic Geometry 11G18, 11F03, 14G35 (Primary) 11F27, 11F30 (Secondary) Let $L$ be an even indefinite lattice. We show that if $L$ splits off a hyperbolic plane and a scaled hyperbolic plane, then the Kudla-Millson lift of genus $1$ associated to $L$ is injective. Our result includes as special cases all previously known injectivity results on the whole space of elliptic cusp forms available in the literature. In particular, we also consider the Funke-Millson twist of the lift. Further, we provide geometric applications on locally symmetric spaces of orthogonal type. |
| title | Injectivity of the genus 1 Kudla-Millson lift on locally symmetric spaces |
| topic | Number Theory Algebraic Geometry 11G18, 11F03, 14G35 (Primary) 11F27, 11F30 (Secondary) |
| url | https://arxiv.org/abs/2312.00572 |