On the geometric side of the Jacquet-Rallis relative trace formula

Abstract: We study some aspects of the geometric side of the Jacquet-Rallis relative trace formula. Globally, we compute each geometric term of the Jacquet-Rallis relative trace formula on the general linear group for regular supported test functions. We prove that it can be described by the regular orbital integral. Locally, we show that the regular orbital integral can be compared with the semisimple orbital integral on the unitary group.