An explicit polynomial in p-adic elliptic polylogarithms contains the depth-3 Chabauty-Coleman-Kim set for rank-at-most-2 elliptic curves, conditional on non-vanishing of a p-adic L-function special value.
Moore, The de R ham period map for punctured elliptic curves and the KZB equation , Annales math \'e matiques du Qu \'e bec (2025), 1--18
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p-adic elliptic polylogarithms and cubic Chabauty
An explicit polynomial in p-adic elliptic polylogarithms contains the depth-3 Chabauty-Coleman-Kim set for rank-at-most-2 elliptic curves, conditional on non-vanishing of a p-adic L-function special value.