Lang-Trotter phenomena and unlikely intersections
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917453346373632 |
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| author | Daw, Christopher Papas, Georgios |
| author_facet | Daw, Christopher Papas, Georgios |
| contents | We show that the Lang-Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber-Pink conjecture for curves in $\mathcal{A}_3$. Unlike previous results for curves in $\mathcal{A}_g$, our result does not rely on any assumption on intersections with the boundary, and in particular applies to potentially compact curves. The argument is based on the $G$-functions method of Yves André. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00759 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lang-Trotter phenomena and unlikely intersections Daw, Christopher Papas, Georgios Number Theory We show that the Lang-Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber-Pink conjecture for curves in $\mathcal{A}_3$. Unlike previous results for curves in $\mathcal{A}_g$, our result does not rely on any assumption on intersections with the boundary, and in particular applies to potentially compact curves. The argument is based on the $G$-functions method of Yves André. |
| title | Lang-Trotter phenomena and unlikely intersections |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.00759 |