Theta correspondence and the Borisov-Gunnells relations
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918340900945920 |
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| author | Branchereau, Romain |
| author_facet | Branchereau, Romain |
| contents | We consider a geometric theta correspondence from the first homology of a modular curve, to modular forms of weight $2$. Using Stevens' description of the homology, we find that this map sends modular symbols to product of weight one Eisenstein series, modular caps to weight $2$ Eisenstein series, and hyperbolic cycles to diagonal restrictions of Hilbert-Eisenstein series. We use it to revisit work of Borisov and Gunnells, and explain its connection to a theorem of Li. In particular, we give a geometric proof of certain relations between Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01473 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Theta correspondence and the Borisov-Gunnells relations Branchereau, Romain Number Theory We consider a geometric theta correspondence from the first homology of a modular curve, to modular forms of weight $2$. Using Stevens' description of the homology, we find that this map sends modular symbols to product of weight one Eisenstein series, modular caps to weight $2$ Eisenstein series, and hyperbolic cycles to diagonal restrictions of Hilbert-Eisenstein series. We use it to revisit work of Borisov and Gunnells, and explain its connection to a theorem of Li. In particular, we give a geometric proof of certain relations between Eisenstein series. |
| title | Theta correspondence and the Borisov-Gunnells relations |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.01473 |