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 André.
From: Georgios Papas [view email]
[v1]
Fri, 1 May 2026 16:18:46 UTC (38 KB)
[v2]
Wed, 24 Jun 2026 16:43:12 UTC (38 KB)
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