$p$-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou

Kazim Büyükboduk, Robert Pollack, Shu Sasaki

Let $p$ be an odd prime. Given an imaginary quadratic field $K=\mathbb{Q}(\sqrt{-D_K})$ where $p$ splits with $D_K>3$, and a $p$-ordinary newform $f\in S_k({\Gamma }_0(N))$ such that $N$…