Gross–Prasad's genericity conjecture for L-packets

Let $G$ be a reductive $p$-adic group and let $\phi$ be a Langlands parameter, with associated L-packet $\Pi_\phi(G)$. A representation is generic if it admits a Whittaker model. Gross–Prasad's conjecture. The L-packet $\Pi_\phi(G)$ contains a generic representation if and only if $L(s,\phi,\operatorname{Ad})$ is regular at $s=1$. This conjecture relates generic representations in L-packets to the adjoint local $L$-function; the forward direction is proved in the paper under the stated hypotheses, and the converse is obtained for unramified parameters.