Abstract
In this thesis, we studied the $H$-distinction for the pair $(G,H) = (U_{2n},Sp_{2n})$. We first derived a formula for period integrals of pseudo-Eisenstein series of $U_{2n}$. With the formula, we gave an upper bound of the $H$-distinguished spectrum in terms of the coarse decomposition by excluding some cuspidal data. Moreover, we gave a refined upper bound by controlling the singular hyperplanes in each of the cuspidal data.