Stable base change from unitary groups in three variables and integral relation of automorphic periods

Let $E$ be a real quadratic field and let $U_E$ be the quasi-split unitary group in three variables associated with $E$. We prove a $p$-adic divisibility between the automorphic periods of a cuspidal automorphic representation $π_U$ of $U_E$ and the periods of its Rogawski stable base change to $\ma