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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21171 |
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| _version_ | 1866909925703155712 |
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| author | Gehrmann, Lennart Guitart, Xavier Masdeu, Marc |
| author_facet | Gehrmann, Lennart Guitart, Xavier Masdeu, Marc |
| contents | We develop the tools required to effectively evaluate the Bianchi rigid meromorphic cocycles introduced by Darmon-Gehrmann-Lipnowski at big ATR points, and use them to obtain the first numerical verification of the conjectured algebraicity of these special values. Moreover, our computations suggest that these special values exhibit behaviour analogous to that of the special values of Borcherds products on Hilbert modular surfaces at big CM points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points Gehrmann, Lennart Guitart, Xavier Masdeu, Marc Number Theory 11G18, 11G15 We develop the tools required to effectively evaluate the Bianchi rigid meromorphic cocycles introduced by Darmon-Gehrmann-Lipnowski at big ATR points, and use them to obtain the first numerical verification of the conjectured algebraicity of these special values. Moreover, our computations suggest that these special values exhibit behaviour analogous to that of the special values of Borcherds products on Hilbert modular surfaces at big CM points. |
| title | Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points |
| topic | Number Theory 11G18, 11G15 |
| url | https://arxiv.org/abs/2511.21171 |