Kudla-Millson lift of toric cycles and restriction of Hilbert modular forms
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914314978328576 |
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| author | Branchereau, Romain |
| author_facet | Branchereau, Romain |
| contents | Let $V$ be quadratic space of even dimension and of signature $(p, q)$ with $p \geq q > 0$. We show that the Kudla-Millson lift of toric cycles - attached to algebraic tori - is a cusp form that is the diagonal restriction of a Hilbert modular form of parallel weight one. We deduce a formula relating the dimension of the span of such diagonal restrictions and the dimension of the span of toric and special cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kudla-Millson lift of toric cycles and restriction of Hilbert modular forms Branchereau, Romain Number Theory Let $V$ be quadratic space of even dimension and of signature $(p, q)$ with $p \geq q > 0$. We show that the Kudla-Millson lift of toric cycles - attached to algebraic tori - is a cusp form that is the diagonal restriction of a Hilbert modular form of parallel weight one. We deduce a formula relating the dimension of the span of such diagonal restrictions and the dimension of the span of toric and special cycles. |
| title | Kudla-Millson lift of toric cycles and restriction of Hilbert modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.16996 |