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arXiv · 2605.00759

Lang-Trotter phenomena and unlikely intersections

Christopher Daw·Georgios Papas
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Abstract

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 Andr\'e.

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Christopher Daw, Georgios Papas. 2026-05-01. Lang-Trotter phenomena and unlikely intersections. https://arxiv.org/abs/2605.00759

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