A refined non-vanishing of the $p$-adic logarithm of a rational point on an abelian variety

Ashay Burungale, Christopher Skinner, Xin Wan

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 $p$-adi…