let $v_n\subset v_{n+1}$ be orthogonal spaces of dimensions $n$ and $n+1$ over a number field $f$, and let $g_n\subset g_{n+1}$ be the associated special orthogonal groups. let $\pi_n$ and $\pi_{n+1}$ be irreducible, cuspidal, tempered, automorphic representations of $g_n(\mathbb{a}_f)$ and $g_{n+1}(\mathbb{a}_f)$. in the early 1990s, gross and d. prasad conjectured that a certain period integral attached to $\pi_n$ and $\pi_{n+1}$ is non-zero if and only if a certain automorphic $l$-function is non-zero at $s=1/2$. recently, a. ichino and t. ikeda have proposed a refinement of this conjecture; they give an explicit formula relating the period integral to the $l$-value. in this talk, we state a similar conjecture for unitary groups, as well as sketch the proof of the first case.