Mazur–Tate–Teitelbaum exceptional zero conjecture

Let $f$ be a newform of even weight $k\geq 2$ for $\Gamma_0(pN)$, where $p$ is prime and $p\nmid N$, and let $\chi$ be a Dirichlet character of conductor prime to $pN$ with $\chi(p)=1$. Let $L_p(f,\chi,s)$ be the associated $p$-adic $L$-function, let $L^{\mathrm{alg}}(f,\chi,k/2)$ be the algebraic part of the central classical $L$-value, and let $\sigma_p(f)$ be the local Galois representation attached to $f$. Exceptional zero conjecture. There exists an invariant $\mathcal{L}_p(f)\in\mathbb{C}_p$, depending only on $\sigma_p(f)$, such that

$$L'_p(f,\chi,\tfrac{k}{2})=\mathcal{L}_p(f)\cdot L^{\mathrm{alg}}(f,\chi,\tfrac{k}{2}).$$

This conjecture relates the first derivative at the exceptional zero of the $p$-adic $L$-function to the central classical $L$-value and is part of the $p$-adic formulation of BSD-type conjectures. The source does not state its resolution.