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Let E/F be a quadratic extension of number fields. Suppose that every real place of F splits in E and let H be the unitary group in 3 variables. Suppose that Π is an automorphic cuspidal representation of GL(3, EA). We prove that there is a form φ in the space of Π such that the integral of φ over H(F )\H(FA) is non zero. Our proof is based on earlier results and the notion, discussed in this paper, of Shalika germs for certain Kloosterman integrals.

Distinguished representations and quadratic base change for 𝐺𝐿(3)