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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12131 |
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| _version_ | 1866916693255651328 |
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| author | Saettone, Francesco Maria |
| author_facet | Saettone, Francesco Maria |
| contents | We prove an equidistribution statement for the reduction of Galois orbits of CM points on the special fiber of a Shimura curve over a totally real field, considering both the split and the ramified case. The main novelty of the ramified case consists in the use of the moduli interpretation of the Cerednik--Drinfeld uniformisation. Our result is achieved by associating to the reduction of CM points certain Hilbert modular forms of weight $3/2$ and by analyzing their Fourier coefficients. Moreover, we also deduce the Shimura curves case of the integral version of the André--Oort conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistribution of CM points on Shimura Curves and ternary theta series Saettone, Francesco Maria Number Theory 11G18 We prove an equidistribution statement for the reduction of Galois orbits of CM points on the special fiber of a Shimura curve over a totally real field, considering both the split and the ramified case. The main novelty of the ramified case consists in the use of the moduli interpretation of the Cerednik--Drinfeld uniformisation. Our result is achieved by associating to the reduction of CM points certain Hilbert modular forms of weight $3/2$ and by analyzing their Fourier coefficients. Moreover, we also deduce the Shimura curves case of the integral version of the André--Oort conjecture. |
| title | Equidistribution of CM points on Shimura Curves and ternary theta series |
| topic | Number Theory 11G18 |
| url | https://arxiv.org/abs/2504.12131 |