Lang-Trotter phenomena and unlikely intersections
Abstract
We show that the Lang-Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber-Pink conjecture for curves in A3. Unlike previous results for curves in Ag, 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.
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