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Investigates p-adic logarithm behaviors in rational points on abelian varieties, suggesting new insights.
Inspired by a beautiful formula of Bertolini, Darmon, and Prasanna—the oft-termed BDP formula —we address questions about the non-vanishing of non-torsion points under p -adic logarithms of abelian varieties. We largely consider situations most applicable to GL₂ GL 2 -type abelian varieties associated with Hilbert modular newforms and Heegner points. Not surprisingly, the main tool employed is the p -adic analytic subgroup theorem.
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Burungale et al. (2026) studied this question.
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